Cho tam giác ABC vuông tại A. Đường cao AH. Biết AB:AC=3:4 và BC=15cm. Tính BH? CH?
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
BA/AC=3/4
nên HB/HC=(3/4)^2=9/16
=>HB/9=HC/16=(HB+HC)/(9+16)=15/25=0,6
=>HB=5,4cm; HC=9,6cm
![](https://rs.olm.vn/images/avt/0.png?1311)
Sử dụng hệ thức về cạnh góc vuông và đường cao trong tam giác vuông, tính được BH =4,5cm, CH = 8cm
![](https://rs.olm.vn/images/avt/0.png?1311)
Lời giải:
Do $AB:AC=3:4$ nên đặt $AB=3a; AC=4a$ với $a>0$
Áp dụng hệ thức lượng trong tam giác vuông:
$\frac{1}{144}=\frac{1}{AH^2}=\frac{1}{AB^2}+\frac{1}{AC^2}=\frac{1}{(3a)^2}+\frac{1}{(4a)^2}=\frac{25}{144a^2}$
$\Rightarrow a^2=25\Rightarrow a=5$ (do $a>0$)
$\Rightarrow AB=3a=15; AC=4a=20$ (cm)
$BH=\sqrt{AB^2-AH^2}=\sqrt{15^2-12^2}=9$ (cm)
$CH=\sqrt{AC^2-AH^2}=\sqrt{20^2-12^2}=16$ (cm) - theo định lý Pitago
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: \(\Delta ABC\) vuông tại A ( Đường cao AH )
Ta thấy \(AB:AC=3:4\)
Mà đây là 2 cạnh góc vuông
\(\Rightarrow\) Đây là bộ số Pytago: \(AB:AC:BC=3:4:5\)
Từ đó ta tính được số đo của \(\left\{{}\begin{matrix}AB=9\\AC=12\end{matrix}\right.\)
Xét \(\Delta ABC\) vuông tại A:
Theo hệ thức lượng trong \(\Delta\) vuông ta được:
+ \(AC^2=HC.BC\Rightarrow HC=\dfrac{AC^2}{BC}=9,6\left(cm\right)\)
+ \(AB^2=BH.BC\Rightarrow BH=\dfrac{AB^2}{BC}=5,4\left(cm\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: AB:AC=3:4
nên \(AB=\dfrac{3}{4}AC\)
Áp dụng hệ thức lượng trong tam giác vuông vào ΔABC vuông tại A có AH là đường cao ứng với cạnh huyền BC, ta được:
\(\dfrac{1}{AH^2}=\dfrac{1}{AB^2}+\dfrac{1}{AC^2}\)
\(\Leftrightarrow\dfrac{1}{\left(\dfrac{3}{4}AC\right)^2}+\dfrac{1}{AC^2}=\dfrac{1}{6^2}=\dfrac{1}{36}\)
\(\Leftrightarrow\dfrac{1}{\dfrac{9}{16}AC^2}+\dfrac{\dfrac{9}{16}}{\dfrac{9}{16}AC^2}=\dfrac{1}{36}\)
\(\Leftrightarrow AC^2\cdot\dfrac{9}{16}=36\cdot\dfrac{25}{16}=\dfrac{225}{4}\)
\(\Leftrightarrow AC^2=100\)
hay AC=10(cm)
Ta có: \(AB=\dfrac{3}{4}AC\)
nên \(AB=\dfrac{3}{4}\cdot10=7.5\left(cm\right)\)
Áp dụng định lí Pytago vào ΔAHB vuông tại H, ta được:
\(AB^2=AH^2+BH^2\)
\(\Leftrightarrow BH^2=7.5^2-6^2=4.5^2\)
hay BH=4,5(cm)
Áp dụng định lí Pytago vào ΔACH vuông tại H, ta được:
\(AC^2=AH^2+HC^2\)
\(\Leftrightarrow HC^2=10^2-6^2=64\)
hay HC=8(cm)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(1,\)
\(a,\) Áp dụng HTL tam giác
\(\left\{{}\begin{matrix}AH^2=CH\cdot BH\\AB^2=BH\cdot BC\\AC^2=CH\cdot BC\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}BH=\dfrac{AH^2}{CH}=\dfrac{25}{6}\left(cm\right)\\AB=\sqrt{\dfrac{25}{6}\left(\dfrac{25}{6}+6\right)}=\dfrac{5\sqrt{61}}{6}\left(cm\right)\\AC=\sqrt{6\left(\dfrac{25}{6}+6\right)}=\sqrt{61}\left(cm\right)\end{matrix}\right.\\ BC=\dfrac{25}{6}+6=\dfrac{61}{6}\left(cm\right)\)
\(b,S_{ABC}=\dfrac{1}{2}AH\cdot BC=\dfrac{1}{2}\cdot5\cdot\dfrac{61}{6}=\dfrac{305}{12}\left(cm^2\right)\)
Lời giải:
Vì $AB:AC=3:4$ nên đặt $AB=3a; AC=4a$ với $a>0$
Áp dụng định lý Pitago:
$AB^2+AC^2=BC^2$
$\Leftrightarrow (3a)^2+(4a)^2=225$
$\Leftrightarrow 25a^2=225$
$\Rightarrow a=3$ (do $a>0$)
Áp dụng hệ thức lượng trong tam giác vuông:
$AB^2=BH.BC\Rightarrow BH=\frac{AB^2}{BC}=\frac{9a^2}{15}=\frac{9.3^2}{15}=5,4$ (cm)
$AC^2=CH.CB\Rightarrow CH=\frac{AC^2}{BC}=\frac{16a^2}{15}=\frac{16.3^2}{15}=9,6$ (cm)
Hình vẽ:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAR0AAADaCAYAAACb8JbDAAAaEElEQVR4Ae2dfXAVVZrG558pLaKFC4aQSEY+MsWHjLqUIoaIJYKDxkjGVEa2YoVFRkYs0CkKC41RxiAVlEEU/BpWqdWKTEqYMBlYRiZoLLCGNS4Di7LlTKAMZsXCWIwszEQW1nfraabbvp2+93bf26c/n1N16957bvc53b/T/dzzvuc9p78jTCRAAiTgI4Hv+FgXqyIBEiABoejwIiABEvCVAEXHV9ysjARIgKLDa4AESMBXAhQdX3GzMhIgAYoOrwESIAFfCVB0fMXNykiABCg6vAZIgAR8JUDR8RU3KyMBEqDo8BogARLwlQBFx1fcrIwESICiw2uABEjAVwIUHV9xszISIAGKDq8BEiABXwlQdHzFzcpIgAQoOrwGSIAEfCVA0fEVNysjARKg6PAaIAES8JUARcdX3KyMBEgg0aJTVSWiv6qrRR58UOTPf+ZFQQIkoJJA4kVHh/vNNyIdHSL33afn8J0ESEAFAYqOhWpNjSWDX0mABDwlQNEx4Xz7bZGtW00Z/EgCJOA5gcSLju7T0d/b2z1nzAJJgARMBBIvOiYW0t0tcvfd5hx+JgES8JoARcdC9M47LRn8SgIk4CkBio4J51tviTQ0mDL4kQRIwHMCiRcd3ZeDOB0IzvHjnjNmgSRAAiYCiRYdEwd+JAES8IkARccn0KyGBEjgPAGKDq8EEiABXwlQdHzFzcpIgARiLzqdnZ2yevVqWbFihXR0dMjZs2fZ6iRAAgESiK3o7N27V0aOHCeFhROlrOxnMnbsw1JaWiGlpWWC35hIgASCIRBL0YGoFBRcIlOndhhLV+hD4+XlnTJ48HAKTzDXG2slAYml6KCHYyc4ZuFBj+fUqVO8BEiABHwmEDvRgQ+nqOjqAT0cXXD0d5ha27Zt8xk3qyMBEoid6DQ3N2s+HF1c0r3DxwPnMhMJkIC/BCg6/vJmbSSQeAKxEx2n5lVJSTnNq8Rf/gQQBIHYiQ4gOnEkFxQMlY0bN8q5c+eC4M46SSCxBGIpOhgyHzp0hEyZYj9kXlBQLBUVFVJVVSVNTU1y8uTJxF4APHES8JtALEUHECE8GBYvLLxSRo9eLGVlD0lJyfVa3pYtW6S+vl4THQgPPh84cMBv9qyPBBJJILaig9bs7++XDRs2yPjx42XcuHGyfv16IzbnxIkTsnz5ckN4ID7t7e00txJ5G/Ck/SQQa9EByIMHDxrCgs/WtGvXLqmpqTG2aWxspLllhcTvJOAhgcSLDlh+/PHHMn/+fEN45s2bp4mVh5xZFAmQwN8JUHT+DuL06dOaUxlmFl7V1dXS1tZGc4u3Cgl4TICiYwEKv47V3IIgMZEACXhDgKJjw7G7u1sWLFhgmFsY3YIJxkQCJJA/AYpOGobo3TQ0NBjCA3OrpaWF5lYaXswmAacEKDoZSCFaedOmTVJbW2uID4bZMdzORAIkkBsBio4Dbj09PQPMrUOHDjnYk5uQAAlYCVB0rETSfEfvBjE8+ugW3mlupYHFbBLIQICikwGO3U8wt+Df0cUHfh+aW3akmEcC9gQoOvZcMuZagwk5dysjLv5IAikEKDopOJx/sQYToufT2toqZ86ccV4ItySBBBKg6OTZ6BAaq7nFpTLyhMrdY02AouNB82IkyxxMWFdXx7lbHnBlEfEkQNHxqF2xjAYWBNMdzOj9wOnMlQk9AsxiYkOAouNhU0JgMIxuNrcQTEhzy0PILCryBCg6CpoQqxCazS2MbjGYUAFoFhlJAhQdRc1mF0y4efNmRbWxWBKIDgGKjuK2sgYTcmVCxcBZfOgJUHR8aCIskwoTS3cyc2VCH6CzitASoOj41DR25hZHt3yCz2pCRYCi43NzwK9jXplw2bJlHN3yuQ1YXbAEKDoB8LfO3UIwIZ+7FUBDsMpACFB0AsEuYjd3CzE+TCQQdwIUnYBb2Dq6hajmvr6+gI+K1ZOAOgIUHXVsHZeMwEGYWProFuduOUbHDSNIgKITkkbDVAnzyoSYSoEZ7Jy7FZIG4mF4RoCi4xlKbwqC0Og9HrxjZUKaW96wZSnhIEDRCUc7pByFNZgQT6Po6upK2YZfSCCqBCg6IW05BBNihrq518NgwpA2Fg/LFQGKjitc/m9sHd1aunQpF4L3vxlYo4cEKDoewlRVFAIHMV9L7/VgHhdMMNVpxowZtlWky7fdmJkkYCFA0bEACetXmFvWxxxv375d6eGmE5d0+UoPhoXHhgBFJ2JN2dbWlrIyIYbZIUgqUjpxSZev4hhYZvwIUHQi2KYIJpw/f75hbsH0wnwur1M6cUmX73X9LC+eBCg6EW1XBBOaF4KHvwcxPl4miEu6l5f1sKxkEaDoRLy97Z675ZW5la5Hky4/4ih5+D4RoOj4BFplNTC3rKNbXiwEn05c0uWrPEeWHR8CFJ2YtCWeu2Wdu4WlMvKZu5VOXNLlxwQlT0MxAYqOYsB+F4+VCc3P3UIwYa7P3UonLuny/T5X1hdNAhSdaLZbxqPu7u5OWQgeI11cmTAjMv7oIwGKjo+w/azKbnQLUyqYSCBoAhSdoFtAcf3t7e0p5hYmkXKpDMXQWXxGAhSdjHji8aN1Ifg5c+YYwYQffvihrF27Vpqbm2XPnj3xOGGeRagJUHRC3TzeHRwWgjcvlTF79mwZO3asDB48WEaPHq29hgwZIpMnT2ZPyDvsLMmGAEXHBkqcs/TRrUsvvVRKSkrkpptuMqKOb775ZiktLdWE5+zZs3HGwHMLkABFJ0D4QVW9detWGTRoUIrgYBgcLwgPejw0tYJqnfjXS9GJfxsPOEP4cMaMGWP0cHTB0d9hbsHHw0QCKghQdFRQDXmZ2URn1KhRFJ2Qt2GUD4+iE+XWy/HY9+/frzmQzf4cvZcD82pQwSD5xYu/yLF07kYCmQlQdDLzie2vI8tGSnFxsUyfPt0wsyA4I0pHyIUXXSjFVxbLo2sflTP/eya2DHhiwRCg6ATDPdBa3/3gXRkxaYRcePGFcsGFFwjMKbyGDB0il11+mRROKJRhE4dJ0cQiubH2Rvn8i88DPV5WHi8CFJ14tWfWs/nL//xFJsyYoInKsB8Mk8effVyeaH5CGpY3yG/e+o18+uWn0tLRImMqxkjhFYWa8IydNla2v6t2PeasB84NYkOAohObpnR2IncsuEMTEgjKfU/cJ8e+Omb7OnT0kMyYO0MTHvR6iq8qlsfWPSbn/u+cs4q4FQmkIUDRSQMmjtlNLzUZgjP1rqnS09djKzhmIVqyeokMv3q4DLvivLk1o26GHP3saBzx8Jx8IkDR8Ql00NXs2b9H8+NAPC6fcrns+XBPVsHRxWdL5xb5/g3fN8ytcTeOk3e63gn6lFh/RAlQdCLacG4O+/RfT8uE6ef9OEU/KJI3dr7hWHB04Tn8+WGZ/s/TDXOr5KoSaVzT6OYwuC0JaAQoOgm4EGbdM8swqxavWuxacHThwfvSZ5ZK8dXFhrl1S90t8vlxjm4l4DLy7BQpOp6hDGdBK/9lpSE45XPKHflxzCJj93nr7q0yZpppdKtirGAYnokEnBCg6DihFNFtuj7qktJJpdrweNkNZXLgyIG8ejlmATrUe0hunntzirnFYMKIXig+HzZFx2fgflX35Vdfyvjp47VeDuJxXtv5mmeCYxafR9Y9IihfH92ae/9crsfjVyNHtB6KTkQbLtth/+j+Hxlm1eKn8vPjmEXG+rnrky4pX1YuJdeUyIirRsitt90qWJnw4MGD2Q6RvyeUAEUnhg3/5EtPGoJTcVeFkh4OxOfol0dl7sa5MuvZWVK5ulLuX3K/8Xx1POYYC4bl89ytGDYNT0lEKDoxuwzM8TijK0bLB90fKBOdtR1r5Za1t8jt62+X9gPtGkk8cQKCo78aGhrEq8ccx6ypEns6FJ0YNT3icSbOnGjMq9qwbYMywdmyb8v5Hs66Sln5bytTKOKRxnjWli489fX1fO5WCqFkf6HoxKj9n3/hefne1d/TTKtJ906Sef86T/Yd3ee58Oz/dL9Ura+S2567TepfrZe+U30DKKJ3g16OLjx4Ry+I5tYAVInLoOjEpMl37dql3eCzbpslN/7TjVL5XKXRE3l97+ueCU/viV5Z2LJQK7vmpRo5+N+ZHcatra1SU1NjiA/NrZhccHmcBkUnD3hh2bW3t1cbMUJvAmYNHjez6f1NUv1CtdYbgd/lqd89JZ/0fZK3+MCU0vw4626Xzf+x2RECPHerrq7OEB6aW46wxXYjik7Em/bMmTOycOFC7Yaurq4W+FP0hF4IzJ/KdZWaUNz9yt3yh8N/yFl43vzgTZn5zEytvIa2BlfLXEAIm5qaDOGhuaW3UvLeKToRb/MXX3zRuJHxCGFrOvHXE9K4tVHzwWBoGy+IhzXeJtv3jz77SGa/MFvrOS14fYGc/NtJa1VZv8Of09bWlvKYY5pbWbHFbgOKToSbtLOz0xCclStXZnTSWs2tpu1NcviLw47EB2aZHo8DBzKc0/kkBA7OmzfPOHaaW/nQjN6+FJ3otZl2xFY/Tn9/f9YzMZtbP1z7Q7nrl3c5Gt2CPwjbIx6n5d9bstbjZAOYWxBKjm45oRWvbSg6EWxPmCkPPvigdsNiZKinp8fxWVjNLfRcMLqFUSk7E2vbf24zRsGatjW58uM4OSj9Mce6+NDcckIt2ttQdCLYfi+//LLRQ9ixY0dOZ2A1t5b/drk2rcEsPDCj4IS+9blbZc6GOTn5cZwcHEa3YGLpwkNzywm16G5D0YlY27333nuGI3bNmjUZ/TjZTs1sbmEYHH4bfXTLHI+DoXdM7FSZEEy4fPlyQ3g4uqWSdrBlU3SC5e+qdvhx9HgXPR7HVQE2G+vmFvw1+ugW/DbNO5qNeJzWrlabPdVkIZgQQ/96r4fmlhrOQZZK0QmSvou64cdZunSpdjPCjwMB8jKZzS3E4ujxOEs3L/Xcj5PtuGluZSMU7d8pOhFpP3M8zvbtah58Zza39HlV6AkFkU6ePMnRrSDA+1AnRccHyPlWAT+Obm7Aj6My6eaWF/E4XhwnBJZzt7wgGZ4yKDrhaQvbIzl27NiAeVW2G3qcefrr0x6XmHtxMLe4VEbu/MK2J0UnbC1iOh7MqzL7cbq7u02/Jusjgh85dysebU7RCXE7muNxVPlxQnz6toeGuCSObtmiiUwmRSekTbV7927j5nr66adDepTBHBbMrQULFhh+LgYTBtMOudZK0cmVnML94Mcxx+NgJIcplQDnbqXyiNI3ik7IWss6ryrJfhwnTYOlMmpra41eD4MJnVALdhuKTrD8B9RujsfZuXPngN+ZMZDAkSNHOHdrIJbQ5lB0QtQ05nlV2dbHCdFhh+JQaG6FohkcHQRFxxEm9RsdP37cMBOw/Cj9OLkxx+qJ5mBCTCKFIDGFhwBFJwRtgXgc8/o4GJ1hyp0AzC1zMCFGupDHFA4CFJ0QtIM5HifX9XFCcBqhOgTrUhlwNqMXBEc9U7AEKDrB8hc4i/V5VfTjeN8YeMCfOZgQUc00Xb3n7KZEio4bWh5vi+Fw3f+AhcqdrHPs8SEkojgsBG9emXDRokXCUITgmp6iExB7ODfNz6uiH0dtQ8DcamxsNHqV6P1gwTCaW2q525VO0bGj4kMelqjQzSpc/Ez+ELCaW5hiwh6mP+z1Wig6Ogkf3+HQ1AUHPgb+2/oIX0Ss5hZGug4cOODvQSS4NoqOz40PX4Ietg8/Tl9fn89HwOpAwGpu4U+Ao1v+XBsUHX84a7WgG6/PjoZPgX4cH+Gnqcpqbq1atYp/BGlYeZVN0fGKpINyzE+0xMXOFA4CVnNrzpw5/ENQ2DQUHYVwzUVjES7dj4PQfPpxzHSC/2w1t9ATxQx2tpP3bUPR8Z7pgBIRgq/H48BpyeC0AYhCk2E1txhM6H3TUHS8Z5pSIuJxzPOADh06lPI7v4SPgNXcQmAh8pi8IUDR8YZj2lLgmNTNKnTXmaJBwM7c4jrV3rQdRccbjralQGR0wWE8ji2i0GdazS344yBITLkToOjkzi7jnhgO1/04iMfhmi4ZcYX6Rztzi+EOuTcZRSd3dmn3hMCY43EY7ZoWVWR+sDO3Nm/eLFgLickdAYqOO16Otjb7cXBhMsWHgNXcwsMQORrprn0pOu54Zd16165dhh+H8ThZcUVyA6u5BfOZ5pbzpqToOGeVdcve3l7jueMYZuW8qqzIIruBnbm1ceNGBhM6aFGKjgNITjbhOsdOKMVvG6u5xdGt7G1M0cnOyNEWzz77rGFWwcRiSg4Bq7mFXm5XV1dyALg8U4qOS2B2m5v9OBAfpuQRsJpbiM9CL4hztwZeCxSdgUxc5Zj9OFh+lPE4rvDFbmM7c4ujW6nNTNFJ5eHqm9WP09PT42p/bhxPAnbmFufcfdvWFJ1vWbj+RD+Oa2SJ2cHO3GLM1vnmp+jkeBvQj5MjuITtZjW38ESKpJtbFJ0cbgL6cXKAluBdrOYWggmRl9RE0XHZ8vTjuATGzTUCduZWUke3KDoubwr6cVwC4+YpBODX0VcfwLD6smXLEmduUXRSLonMX+jHycyHvzojgHla5tUk6+rqEvXcLYqOs+tE6MdxCIqbOSKAeC4s7KYv8ob3lpYWR/tGfSOKjoMWpB/HASRukhMB6+gWhCjuE4UTITrXTrtWJt0wSZ7a9JRsen+T61f9knptf5TR8HxDyv4n/3Yyp4uNO5GATgCBgzCx9F4PPsd5dCv2orP17a1SNLFIe017eJpUrqt09bpu0XXG/hPunJCy7+3rb9cESL94+E4CuRJA7A5ieHThwXO3WltbYzl3K/ai8+tdv9ZEo/CKQrn+oetl5jMzHb9uePwGGf6PwwX7jigfIdNXTU/ZFwKGnhMTCXhFAEKjCw/eGxoaYmduRU50du8WqaoSee89Z81sFp1XfvuKHPvqmKPX0S+Oyk/u+4nMnDVTKu+olK4Pu1L2g3hRdJy1AbdyR8AaTFhbWxurpTIiJzpPPy2yZo0I3p2kXEWnaVWTJjgQnTfb30wRHAgXRccJfW6TKwEEE2JBMHOvJ4hgwj/9SaShQaSmRmTDBhEvnr4TKdE5d+78yX/9tUhtrQi+Z0u5iA5EBmKDF8THrndE0clGnr97QcA6uoWF4CFIfqRPPxW55x6RfftEvvlG5KuvRH7+c5G33sqv9kiJzvvvi6xadf6EV6wQ2bs3+8m7FZ19/7VPZtfM1gRn7vy5cvjYYYpOdszcQiEBPMII87X0Xg9WJvRjdAvWREdH6on19Yk891xqnttvkRIdmFXvvHP+FAED37MlN6KTzY9j7vGwp5ONPH/3kgB6N3Aq68KD0S3Vjzn+8Y9FYFV4nSIjOujeAQKcyPoLJhbyMyU3opPNj0PRyUSav/lBAI+qhuDo4oNhdlXmVnW1mjOKjOhgnevGxlQIjz4qApMrU3IqOk78OBSdTKT5m18EEExonrul6rlbdXUi/f0Dz8oub+BW6XMiIzqwI63D5Bg+z7YOuhPRcerHoeikv5D4i78EEExonbuFGB8v09q1A306R46I/PSn+dUSCdGBCXXvvQNNKeTPnz8w34wkm+i48eNQdMxk+TkMBCA0ZnMLfh+vzK1PPhGprxf54x/Pn2lvr8iiRSI7duR35pEQnXxOMZvouPHjUHTyaQnuq4oAzC3r6JZXC8FDcB54QAT+nblzRdrb8z+LRIuOWz8ORSf/C44lqCHQ398/YO4WlsoI43O3Eis6ufhxKDpqbhiW6h0BrExoNrcwuhW2pTISKTq5+nEoOt7dHCxJHYHu7m5BAKE+rI6lMsL0mONEik6ufhyKjrobhSV7S8BudOu1114LhbkVe9FpWtMkFw+/WAqGFciSFUvkV22/yjqvyiwu6T4zItnbm4SlqSHQ3t6eYm5h7pb5uVudnZ2yevVqWbFihXR0dMjZs2fVHIip1NiKzt69e2XkyHHyD0PGyahRi6Ws7CEZVnStFBQMkclTJkumeVXphMacT9ExXUX8GGoC1oXgFy5cKFu2bNHuj8LCiVJW9jMZO/ZhKS2tkNLSMsG9ozLFUnQAraDgEpk6tcOYMqFPnSgv75QLLrhENr6x0XYip1lYMn2m6Ki8LFm21wSwELy+MmFFRYV897uDpLz897b3x+DBw5UKTyxFBz0cO8ExC0/JZaOk+7PunIWHouP1bcHy/CCApTIuuuhSmTJl5wDBMd8f6PGcOnVKySHFTnRgoxYVXZ0WqA62aPhkeeCxBwSrCebywtKnWHMZi71jmQG+yCAK18Crr74qQ4dOzHp/wNTatm0bRccJgebmZs1G1cUl3Tt8PHAuY/3jXF9Y8B1PiNCHJvleRRZV4WYwfvx4GT16cVbRgY8HzmUVKXY9HTeic1HRRcaTHvQnRrh9v2baNbzRQn6j8c/gWyGk6CiQUafm1fDi6+SRJx8RzM3K57Vv/z6aVjQvI3MNwLwqLLwya0+H5pVLcXLiSFbpKHN5uNycBHwlEPT9ETvzCq2HIfOhQ0fIlCn2Q+ZFRepjEXy9ilgZCbggEPT9EUvRAX+ARW8GI1l+Bz+5aH9uSgKBEAjy/oit6KAlMd0fod1wLsMTjyFAVbEHgVw5rJQE8iAQ1P0Ra9HJoz24KwmQgCICFB1FYFksCZCAPQGKjj0X5pIACSgiQNFRBJbFkgAJ2BOg6NhzYS4JkIAiAhQdRWBZLAmQgD0Bio49F+aSAAkoIkDRUQSWxZIACdgToOjYc2EuCZCAIgIUHUVgWSwJkIA9AYqOPRfmkgAJKCJA0VEElsWSAAnYE6Do2HNhLgmQgCICFB1FYFksCZCAPQGKjj0X5pIACSgiQNFRBJbFkgAJ2BOg6NhzYS4JkIAiAhQdRWBZLAmQgD0Bio49F+aSAAkoIkDRUQSWxZIACdgToOjYc2EuCZCAIgIUHUVgWSwJkIA9AYqOPRfmkgAJKCLw/y0uqru49gQlAAAAAElFTkSuQmCC)