A tangent is drawn from a point that is at a distance of 37 cm from center of the circle O, and diameter is 24 cm. The length (in cm) of the tangent is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 35.
A point P is located 37 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 = 37 cm (distance from the center to the point)
OT = 12 cm (radius of the circle)
PT is the length of the tangent
In triangle OPT:
⇒ OP² = OT² + PT²
⇒ 37² = 12² + PT²
⇒ 1369 = 144 + PT²
⇒ PT² = 1369 - 144
⇒ PT² = 1225
⇒ PT = √1225
⇒ PT = 35 cm
Therefore, the length of the tangent is 35 cm.