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Question Number 198933 by cherokeesay last updated on 25/Oct/23

Commented by mr W last updated on 26/Oct/23

Commented by Rasheed.Sindhi last updated on 26/Oct/23

$T han k s for help in diagram sir!$
	Answered by Rasheed.Sindhi last updated on 26/Oct/23

	$R i g h t v e r t e x o f y e l l o w t r i a n g l e = D (s a y)$ $I n t e r s e c t i o n o f \vec{D C} & \vec{B A} = E$ $B E i s d i a m e t e r = 2 r [∵ B D E i s r i g h t t r i a n g l e]$ $C E = C B = \sqrt{3^{2} + 4^{2}} = 5$ $D E = D C + C E = 3 + 5 = 8$ $△ B D E :$ ${B E}^{2} = {B D}^{2} + {D E}^{2}$ ${(2 r)}^{2} = 4^{2} + 8^{2} = 80$ $r^{2} = 20 \Rightarrow r = A B = 2 \sqrt{5}$ $△ A B C :$ ${A C}^{2} = {B C}^{2} - {A B}^{2} = 5^{2} - {(2 \sqrt{5})}^{2} = 5$ $A C = \sqrt{5}$ $▴ A B C = \frac{1}{2} \cdot A B . A C$ $= \frac{1}{2} (2 \sqrt{5}) (\sqrt{5}) = 5 {cm}^{2}$
	Commented by cherokeesay last updated on 26/Oct/23

	$S o n i c e!$ $t h a n k y o u s i r!$
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