Question

Given the circle below with secants PQR and TSR, find the length of PQ. round to the nearest tenth if necessary

Answer 1

PQ ≈ 20.5

Explanation:

The product of lengths from R to the intersection points with the circle is the same for each secant:

RS×RT = RQ×RP

40(40 +31) = (44)(PQ +44)

40(71)/44 = PQ +44

PQ = 2840/44 -44 = 64 6/11 -44 = 20 6/11

PQ ≈ 20.5