isi-entrance 2019 Q20

isi-entrance · India · UGA Circles Inscribed/Circumscribed Circle Computations

In the following picture, $A B C$ is an isosceles triangle with an inscribed circle with center $O$. Let $P$ be the mid-point of $B C$. If $A B = A C = 15$ and $B C = 10$, then $O P$ equals:
(A) $\frac { \sqrt { 5 } } { \sqrt { 2 } }$
(B) $\frac { 5 } { \sqrt { 2 } }$
(C) $2 \sqrt { 5 }$
(D) $5 \sqrt { 2 }$.

In the following picture, $A B C$ is an isosceles triangle with an inscribed circle with center $O$. Let $P$ be the mid-point of $B C$. If $A B = A C = 15$ and $B C = 10$, then $O P$ equals:\\
(A) $\frac { \sqrt { 5 } } { \sqrt { 2 } }$\\
(B) $\frac { 5 } { \sqrt { 2 } }$\\
(C) $2 \sqrt { 5 }$\\
(D) $5 \sqrt { 2 }$.

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