Question

A circle with centre 'O', 'P' is a point outside the circle and PA and PB are two tangents to the circle at the point of contacts 'A' and 'B' from 'P'. If the length of PA 10 cm, then the length of PB =

• A. 5 cm
• B. 20 cm
• C. 10 cm
• D. 2.5 cm

Answer 1

The Correct Option is C

To solve the problem, we need to find the length of the tangent segment PB drawn from an external point P to a circle, given that PA is another tangent from the same point and its length is 10 cm.

1. Understanding the Property of Tangents from a Point:
If two tangents are drawn to a circle from the same external point, then the lengths of those tangents are equal.
This means:

$ PA = PB $

2. Using the Given Information:
We are given that:

$ PA = 10 \, \text{cm} $

3. Applying the Tangent Length Property:
Since $ PA = PB $, we substitute:

$ PB = 10 \, \text{cm} $

Final Answer:
The length of PB is $ 10 \, \text{cm} $.