Chapter 10.3, Problem 6PSA

To determine

To Prove : $\stackrel{⌢}{AB}\cong \stackrel{⌢}{AC}$

Answer to Problem 6PSA

1

Explanation of Solution

Given information : $\text{A circle with centre D, }\angle B\cong \angle C$

  

  $\begin{array}{l}\text{As }\angle B\cong \angle C\\ \Rightarrow AB\cong AC\text{ [Sides opposite to equal angles are equal]}\\ \text{In }\Delta \text{ABD and }\Delta \text{ACD}\\ AD\cong AD\text{(common)}\\ BD\cong CD(\text{radii})\\ \angle APB\cong \angle ADC(90°)\\ \text{By RHS congruency}\\ \Delta ADB\cong \Delta ADC\\ \Rightarrow AB\cong AC\\ \Rightarrow \stackrel{⌢}{AB}\cong \stackrel{⌢}{AC}\text{[Equal chords intercepts equal arcs]}\end{array}$