Question

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.Choose the correct alternative.
(A) 25 cm
(B) 24 cm
(C) 7 cm
(D) 14 cm

Answer 1

Final Answer : 7 cm

Steps:

1) Let external point be B, & OA be radius of circle.

Given:

OB = 12.5cm

AB = 12cm

In right traiangle , ΔAOB, by Pythagoras Theorem ,

$OA=\sqrt{AB^{2}-OB^{2}} \\ \\ => \sqrt{12.5^{2}-12^{2}} \\ \\ =>\sqrt{12.25} = 3.5 \:\:units$

Hence,Diameter =2*3.5=7 cm

Answer 2

Answer:

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