In the given figure, $A B=B C=10 \mathrm{~cm}$. If $A C=7 \mathrm{~cm}$, then the length of $B P$ is

Question

In the given figure, $A B=B C=10 \mathrm{~cm}$. If $A C=7 \mathrm{~cm}$, then the length of $B P$ is :

Professor PC Thomas Classes · Answer

(c): $A \mathrm{~s}, A B=B C$ (Given)\ $\Rightarrow A P+B P=B Q+Q C$\ $\Rightarrow \quad A P=Q C \quad[\because B P=B Q$ (Length of tangents from an external point are equal)]\ Let $A P=Q C=x$\ $\Rightarrow A R=R C=x$\ $[\because A P=A R, Q C=R C]$\ As, $A C=7 \mathrm{~cm}$\ $\Rightarrow A R+R C=7 \Rightarrow x+x=7 \Rightarrow 2 x=7$\ $	herefore \quad x=3.5 \quad 	herefore \quad B P=A B-A P=10-3.5=6.5 \mathrm{~cm}$\