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Question Number 51869 by prakash jain last updated on 31/Dec/18

Commented by prakash jain last updated on 31/Dec/18

$Correct answer given is 2 / 9 .$ $I think mininum is 0 .$
	Answered by tanmay.chaudhury50@gmail.com last updated on 31/Dec/18

	$A B = 1 B C = 1 A C = \sqrt{2}$ $l e t B (0, 0) C (1, 0) A (0, 1) p (h, k)$ $e q n o f s t l i n e A C i s x + y = 1$ $h + k = 1 [\frac{h + k}{2} ⩾ \sqrt{h k} \frac{1}{2} ⩾ \sqrt{h k} s o \frac{1}{4} ⩾ h k]$ $a r e a o f △ A P Q = \frac{1}{2} \times h \times k ⩽ \frac{1}{2} \times \frac{1}{4}$ $a r e a A P Q ⩽ \frac{1}{8} {(a r e a A P Q)}_{m a x} = \frac{1}{8}$ $a r e a P Q B R = h k ⩽ \frac{1}{4} (a r e a {P Q B R}_{m a x} = \frac{1}{4})$ $a r e a P R C = a r e a A B C - a r e a A P Q - a r e a P Q B R$ $= \frac{1}{2} \times 1 \times 1 - \frac{1}{2} \times h \times k - h k$ $= \frac{1}{2} - \frac{3}{2} \times h k$ $n o w \frac{1}{2} - \frac{3}{2} \times h k ⩾ \frac{1}{2} - \frac{3}{2} \times \frac{1}{4}$ $(\frac{1}{2} - \frac{3}{2} h k) ⩾ \frac{1}{8}$ $m a x a r e a A P Q = \frac{1}{8}$ $m a x a r e a P Q B R = \frac{1}{4}$ $m i n a r e a P R C . = \frac{1}{8}$ $i c o u l d n o t u n d e r s t a n d t h e q u e s t i o n$ $h o w e v e r i h a v e c a l c u l a t e d t h e a r e a$ $p l s c h e c k . . .$
	Commented by prakash jain last updated on 01/Jan/19
	Thanks. The question was asked in my son fiitjee pre NEW main test. I could not understand the question either.
	Commented by peter frank last updated on 01/Jan/19

	$h e l p m e Q n 51901 Q n 51817$
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