AB is a diameter of a circle The length of AB=5cm If O is the centre of the - Maths - Circles

Question

AB is a diameter of a circle The length of AB=5cm If O is the
centre of the circle and the length of tangent segment AT=12cm ,
determime CT ?

Ajanta Trivedi · Accepted Answer

given : AB= 5 cm and AT= 12 cm

since ABT is a right angled triangle.

$A B^{2} + B T^{2} = A T^{2} 5^{2} + B T^{2} = 12^{2} B T^{2} = 12^{2} - 5^{2} = 144 - 25 B T^{2} = 119$

if a secant and a tangent of a circle are drawn from a point outside the circle, then the product of the lengths of the secant and its external segment equals the square of the length of the tangent segment.

therefore $B T^{2} = C T \cdot A T$

$119 = C T \cdot 12 C T = 119 / 12 c m$

hope this helps you.

AB is a diameter of a circle. The length of AB=5cm. If O is the centre of the circle and the length of tangent segment AT=12cm , determime CT ?