A point P is 13 cm away from the center of a circle. A tangent is drawn from P to the circle, and its length is 12 cm. What is the area of the circle?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 25π cm2.
Let radius = r cm
The radius of a circle is always perpendicular to the tangent line at the point of contact.
In ΔOAP, ∠OAP = 90°
r2 + 122 = 132
⇒ r2 + 144 = 169
⇒ r2 = 25
⇒ r = 5 cm
Area of circle = πr2 = π(5)2 = 25π cm2