MAHARASHTRA Class 10: Construction of Tangents Videos | Construction of Tangents

The line joining the centre of a circle to the external point bisects the angle between two tangents and two radii. 

2∠XAO = ∠XAY

By Pythagoras' theorem, 

13² = 12² + radius²

radius² = 25

radius = 5 cm

As the radius is perpendicular to the tangent, 

By Pythagoras' theorem,

5² = 3² + AX²AX² = 16

AX = 4