Question

ill figure diameter AB of the circle is 12 cm long and tangent segment BT is 5 centimeters. if O is the centre find the measure of AC

Answer 1

Since AB is the diameter and PB is the tangent.

So, AB ⊥ PB (Radius of the circle is perpendicular to the tangent through point of contacy)

⇒ ABC is a right triangle right angled at B

⇒ AT2 = AB2 + BT2 = (5 cm)2 + (12 cm)2 = 25 cm2 + 144 cm2 = 169 cm2 (Pythagoras theorem)

⇒ AT = 13 cm

Now, we know that

If PAB is a secant to a circle intersecting the circle to A and B and PT is a tangent, then PA × PB = PT2

Here is the link for the same.

https://www.meritnation.com/ask-answer/question/dear-meritnation-experts-plz-answer-my-question-if-pab-i/circles/1726596

So,

BT2 = CT × AT

⇒ 144 cm2 = CT × 13 cm

⇒ CT = 144/13 cm