Question

Segment AB is tangent to T at B. What is the radius of T?

Answer 1

The value of the radius of T is 28 units

How to determine the value of the radius of T

From the question, we understand that:

Segment AB is tangent to T at B

This means that

<ABT = 90

So, we have a right triangle

Let the radius of the triangle be r

By the Pythagoras theorem, we have

AT^2 = AB^2 + VT^2

This gives

(25 + r)^2 = 45^2 + r^2

Open the bracket

625 + 50r + r^2 = 2025 + r^2

Subtract r^2 from both sides of the equation

625 + 50r = 2025

Subtract 625 from both sides of the equation

50r = 1400

Divide both sides by 50

r = 28

Hence, the value of the radius of T is 28 units

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