Question

11. A line segment through a point P cuts a given circle in 2 points A & B, such that PA = 16 & PB = 9, find
the length of tangent from points to the circle
(A) 7
(B) 25
(C) 12
(D) 8​

Answer 1

Length of Tangent from Point is 12

Step-by-step explanation:

Given, Length of PA = 16

Length of PB = 9

We know that, if T is any point of Tangency,

then

$PA \times PB = PT^2$

So, Applying the formula here, we get -

$16 \times 9 = PT^2$

⇒ $\sqrt 16\times9 = PT$

⇒ $\sqrt 4\times4\times3\times3 = PT$

⇒ $4\times 3 = PT$

⇒ PT = 12

Hence, Length of Tangent from Points to the circle is 12

Answer 2

Solution

Given that : PA = 16 , PB = 9 .

If point of tangency is T then

PB × PA = PT² .

So,

16 × 9 = PT² .

PT = √144 .

PT = 12 .