Question

11) Length of a tangent segment drawn from a point which is at a distance 12.5 cm from the
centre of a circle is 12 cm, find the diameter of the circle
a) 24cm
b) 25cm
.c) 7cm
d) 14cm​

Answer 1

Step-by-step explanation:

Option C is correct .i.e., Diameter of circle = 7 cm

Step-by-step explanation:

Given: Length of tangent from an external point= 12 cm

Distance between center and exterior point = 12.5 cm

To find: Diameter of circle.

Let say the exterior point be C from where an tangent is drawn to circle with center O.

Tangent touches the circle at point A

⇒ AC = 12 cm and OC = 12.5 cm

In Δ AOC

∠OAC = 90° ( tangent and radius are perpendicular to each other )

So, by Pythagoras theorem

OC² = OA² + AC²

12.5² = OA² + 12

156.25 = OA² + 144

OA² = 156.25 - 144

OA² = 12.25

OA = √12.25

OA = 3.5

⇒ radius = 3.5 cm

⇒ Diameter = 2 × 3.5 = 7 cm

Therefore, Option C is correct .i.e., Diameter of circle = 7 cm

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