Question

In the given figure, if PQ = 6, QR = 10, PS = 8 find TS.

Answer 1

Using the theorem of chords intersecting outside the circle, we have
PT × PS = PR × PQ
⇒ (TS + PS) × PS = (QR + PQ) × PQ
⇒ (TS + 8) × 8 = (10 + 6) × 6
⇒ 8TS + 64 = 16 × 6 = 96
⇒ 8TS = 96 − 64 = 32
⇒ TS = \[\frac{32}{8}\] = 4 units