Question

The circle is inscribed in the triangle. Find the length of AB.

A. 14 cm
B. 17 cm
C. 23 cm
D. 27 cm

Answer 1

(C)23cm

Explanation:

We apply the theorem that tangents to a circle from a given point are equal.

Let X, Y and Z be the tangent points as shown in the attached circle.

By the theorem above:

|CX|=|CY|=4cm

|BY|=|BZ|=10cm

Since |AC|=17cm and |CX|=4cm

|AX|+|CX|=17

|AX|+4=17

|AX|=17-4=13cm

By the same theorem, |AX|=|AZ|

Therefore:

|AB|=|AZ|+|BZ|=13+10=23 cm