Question

Find the value of x. Segments that appear to be tangent are tangent.AX - 2450B no

Answer 1

Solution:

Given:

From the two tangent theorem, if two tangent segments are drawn to one circle from the same external point, then they are congruent.

This implies that

$AB=CB$

where

$\begin{gathered} AB=x-24 \\ CB=50 \end{gathered}$

By substitution, we have

$\begin{gathered} x-24=50 \\ add\text{ 24 to both sides of the equation,} \\ x-24+24=50+24 \\ \Rightarrow x=74 \end{gathered}$

Hence, the value of x is evaluated to be 74

The correct option is