Question

In the given figure, AB is a diameter of the circle. The length of AB = 5 cm. If O is the centre of the circle
and the length of tangent segment AT = 12 cm, determine CT.​

Answer 1

Answer:

Step-by-step explanation:

Given data:

• Diameter of circle = 5 cm
• Length of tangent segment = 12 cm

Construct the triangle by joining  BC and AT.  

Solution:

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

Let CT be x therefore AC is 13-x

Angle ABC=90 degrees  (Angle in a semicircle)

Therefore by Pythagoras 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 +26 x = 144 (x^2 on both sides cancels out)

Therefore CT = x =144/13 = 11.07 cm

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