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Question Number 185907 by Mingma last updated on 29/Jan/23

	Answered by HeferH last updated on 29/Jan/23

	$I f y e l l o w = o r a n g e t h e n$ $A r e a (A C B) = A r e a (P Q R S) .$ $l e t O b e t h e c e n t e r o f t h e s e m i c i r c l e .$ $O P = a$ $A O = R$ $r a d i u s o f i n c i r c l e = r$ $i . {(R + r - a)}^{2} + {(R + r + a)}^{2} = {(2 R)}^{2}$ $a^{2} = R^{2} - r^{2} - 2 R r$ $i i . {P S}^{2} = A r e a (P Q R S) = A P \cdot P B = R^{2} - a^{2}$ $= R^{2} - R^{2} + r^{2} + 2 R r = r^{2} + 2 R r$ $i i i . A r e a (A C B) = \frac{(R + r + a) (R + r - a)}{2} =$ $\frac{{(R + r)}^{2} - a^{2}}{2} = \frac{2 r^{2} + 4 R r}{2} = r^{2} + 2 R r$ $i v . A r e a (A C B) = A r e a (P Q R S)$ $\Rightarrow Y e l l o w = O r a n g e ✓$
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