Chapter 10.4, Problem 18PSB

To determine

To Find : $\stackrel{⌢}{BR}\cong \overline{RC}$

Answer to Problem 18PSB

  $\stackrel{⌢}{BR}\cong \overline{RC}$

Explanation of Solution

Given information : $\Delta ABC\text{ is isosceles, with base }\overline{BC}.$

  

  $\begin{array}{l}\text{As AP = PQ (}\because \text{As the length of tangents drawn)}\\ \text{CP = CR }\mathrm{.....}\text{(1) [From an external point to a circle are equal]}\\ \text{RB = BQ }\mathrm{....}\text{(2)}\\ \text{RB = AC (}\because \text{ABC is isosceles)}\\ \text{AP + PC = AQ + QB}\\ \text{PC = QB }\mathrm{.....}\text{(3)}\\ \therefore \text{By (1), (2) and (3), we get}\\ \overline{\text{BR}}\cong \overline{\text{RC}}\end{array}$