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Question Number 200475 by Rupesh123 last updated on 19/Nov/23

	Answered by deleteduser1 last updated on 19/Nov/23

	$\frac{2 s i n 20}{P C} = \frac{1}{A C} \Rightarrow \frac{P C}{A C} = 2 s i n 20$ $L e t ∠ P B C = x; \frac{s i n x}{P C} = \frac{c o s 10}{B C} \Rightarrow B C = \frac{P C c o s (10 °)}{s i n (x)}$ $\frac{s i n (20 + x)}{A C} = \frac{s i n 50}{B C} = \frac{s i n 50 s i n x}{P C c o s 10} \Rightarrow \frac{P C}{A C} = \frac{s i n 50 s i n x}{c o s (10) s i n (20 + x)}$ $\Rightarrow 2 s i n 20 = \frac{s i n 50 s i n x}{c o s 10 s i n (20 + x)} \Rightarrow \frac{s i n x}{s i n (20 + x)} = \frac{2 s i n 20 c o s 10}{1 - 2 {s i n}^{2} 20}$ $\Rightarrow x = 60 \Rightarrow ∠ P C B = 20 ° \Rightarrow ∠ B C A = ∠ B A C = 50 °$ $\Rightarrow A B = B C$
	Commented by Rupesh123 last updated on 19/Nov/23
	Nice one, sir!
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