43.7k views
4 votes
The circle is inscribed in the triangle. Find the length of AB.

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

The circle is inscribed in the triangle. Find the length of AB. A. 14 cm B. 17 cm-example-1

1 Answer

2 votes

Answer:

(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

The circle is inscribed in the triangle. Find the length of AB. A. 14 cm B. 17 cm-example-1
User Adam Tanner
by
5.5k points