If SA and SB are tangents to a circle from an outside point S, such that SA = 12 cm and angle ASB = 60°. What will the length of chord AB be?

Correct option is A

Given:

SA = 12 cm

∠ASB = 60°

The measure of angles formed opposite to equal lengths of a triangle are same.

Solution:

In the above figure,

SB = SA,

=> ∠ ABS = ∠ BAS 

In Δ ABS,

=> ∠ BAS + ∠ ABS + ∠ ASB = 180°

=> ∠ BAS + ∠ BAS = 180 - ∠ ASB

=> 2 ∠ BAS = 180° - 60° = 120°   

=> ∠ BAS = $$\frac{120}2$$​ = 60°

So, ΔSAB is an equilateral triangle

AB = AS = 12 cm

∴ The length of chord AB be is 12 cm.