In Fig. 10.102, QR is a common tangent to the given circles touching externally at the point T. The tangent at T meets QR at P. If PT = 3.8 cm, then the length of QR (in cm) is

Question

Philoid · Accepted Answer

Given:

PT = 3.8 cm

Property 1: If two tangents are drawn to a circle from one external point, then their tangent segments (lines joining the external point and the points of tangency on circle) are equal.

By property 1,

PQ = PT (Tangent from P)

PR = PT (Tangent from P)

Now,

QR = PQ + PR

⇒ QR = PT + PT

⇒ QR = 3.8 cm + 3.8 cm

⇒ QR = 7.6 cm

Hence, QR = 7.6 cm