A tangent is drawn from a point at a distance of 25 cm from the Centre of a circle C(0, r) of radius 7 cm. The length of the tangent is _____ cm.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 24.
A point P is located 25 cm away from the center O.
A tangent line is drawn from point P to the circle, touching it at point T.
This creates a right-angled triangle OPT, where:
OP = 25 cm (distance from the center to the point)
OT = 7 cm (radius of the circle)
PT is the length of the tangent.
In a right angle triangle OTP:-
⇒ OP² = OT² + PT²
⇒ 25² = 7² + PT²
⇒ 625 = 49 + PT²
⇒ PT² = 625 - 49
⇒ PT² = 576
⇒ PT = √576
⇒ PT = 24 cm
Therefore, the length of the tangent is 24 cm.