Chapter 10.2, Problem 10PSB

To determine

To prove: that the $\Delta ADE$ is isosceles and it is inscribed in the circle.

Answer to Problem 10PSB

  $\Delta ADE$ is isosceles.

Explanation of Solution

Given:

  

Concept used:

Isosceles triangle has two same side and one side different.

Perpendicular from center to the chord bisects the chord.

Calculation:

According to the given:

  $\begin{array}{l}EF\perp AC\text{ and }FD\perp AB.\\ \Rightarrow AE=EC\text{}\text{ and }AD=DB.\end{array}$

Perpendicular from center to the chord bisects the chord.

Also, from the given:

  $\begin{array}{l}AB=AC.\\ \Rightarrow \frac{AB}{2}=\frac{AC}{2}.\\ \Rightarrow AD=AE.\end{array}$

Hence, $\Delta ADE$ is isosceles.