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

A. (q+r)...

Question

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

A. (q+r)^2 / (qr)
B. qr / (q+r)
C. sqrt(q^2 + r^2)
D. (q+r) / (2qr)

Accepted Answer

PS = qr / (q + r) PS is the angle bisector from vertex P in triangle PQR, splitting angle QPR into two equal parts of 60 degrees each, making angle QPR = 120 degrees. We label the sides PQ = r and PR = q (or vice versa, following the standard convention). The angle bisector length formula directly gives PS in terms of the two sides adjacent to P.

In a triangle PQR, PS is the angle bisector of angle QPR and angle QPS = 60 degrees. What is the length of PS? A. (q+r)^2 / (qr) B. qr / (q+r) C. sqrt(q^2 + r^2) D. (q+r) / (2qr)