GATE | GATE-CS-2015 (Set 2) | Question 65

In a triangle PQR, PS is the angle bisector of ∠ QPR and ∠ QPS = 60°. What is the length of PS?

(A) a
(B) b
(C) c
(D) d


Answer: (B)

Explanation:

Area of a Δ = 1/2 * ac sinB 
            = 1/2 * bc sinA 
            = 1/2 ab sinC

Here area (ΔPQR) = area (ΔPQS) + area (ΔPRS)

1/2 rq sin120 = 1/2 PS * r sin60 + 1/2 PS * q sin60

=> PS = rq/(r+q)

There seems to be something wrong with question as it says ∠ QPS = 60°. The question is same on GATE official site paper.

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