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 ?

Answer 1

`CT=11.08\ cm`

Explanation:

step 1

Find the length BT in the right triangle ABT

Applying Pythagoras Theorem

`BT^2=AB^2+AT^2`

substitute the given values

`BT^2=5^2+12^2`

`BT^2=169`

`BT=13\ cm`

step 2

Find the length CT

Applying the Intersecting Secant-Tangent Theorem

we have that

`AT^2=BT(CT)`

substitute the given values and solve for CT

`12^2=13(CT)`

`CT=144/13\\CT=11.08\ cm`