Chapter 10.4, Problem 1PSA

To determine

To Prove : $\text{Length of }\overline{\text{AC}}$

Answer to Problem 1PSA

  $\text{Length of }\overline{\text{AC}}=17\text{ cm}$

Explanation of Solution

Given information : $\text{Radius = 8 cm, BC = 15 cm}$

  

  $\begin{array}{l}\text{Join A to B}\\ \Rightarrow \angle \text{ABC}=90°\text{ [Line through centre to point of contact is perpendicular]}\\ \Rightarrow \Delta \text{ABC is right angled triangle}\\ \Rightarrow {\text{AC}}^{\text{2}}\cong A{B}^2+B{C}^2\\ \Rightarrow A{C}^2\cong 8^2+{15}^2\\ \Rightarrow A{C}^2\cong 289\\ \Rightarrow AC=17\text{ cm}\end{array}$