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 BT=12cm , determime CT ?

Answer 1

Answer:Given - AB is a diameter, AB=5cm and BT=12cm , Bt is a tangent

To Find - CT = ?

Construction - Join BC  

Solution- In triangle ABT by pythagores theorem AT = 13 ( ABT = 90 degrees, Tangent perpendicular to radius)  

Let CT be x therfore AC is 13-x

Angle ABC=90 degrees  (Angle in a semicircle)

Therefore by pythagores theorem  

AB^2-AC^2=CB^2 - (A)

BT^2-CT^2=CB^2 - (B)

From A and B -->

25 - (13-x)^2 = 144 - x^2

25 - 169 +26x = 144 (x^2 on both sides cancels out)

Therefore CT = x =144/13 = 11.07 cm

Step-by-step explanation:

Answer 2

The length of CT is 11.07 cm.

Given,

AB is a diameter, AB=5cm and BT=12cm , Bt is a tangent

To Find,

The length of CT.

Solution,

To solve this question we have to join BC.

Now,  

In triangle ABT, we will apply Pythagoras theorem

AT = 13

Let us assume the length of CT be x, therefore AC is 13-x

Angle ABC=90 degrees  (Angle in a semicircle)

Therefore applying Pythagoras' theorem  

AB²-AC² = CB²

BT²-CT² = CB²

Equating both the above-written equations as they as same R.H.S.

So,

25 - (13-x)² = 144 - x²

25 - 169 +26x = 144

CT = x =144/13 = 11.07 cm

Hence, the length of CT is 11.07 cm.