WBJEE · Maths · Properties of Triangles
\(A B C\) is an isosceles triangle with an inscribed circle with centre \(O\). Let \(P\) be the midpoint of \(B C\). If \(A B=A C=15\) and \(B C=10\), then \(\mathrm{OP}\) equals
- A \(\frac{\sqrt{5}}{\sqrt{2}}\) unit
- B \(\frac{5}{\sqrt{2}}\) unit
- C \(2 \sqrt{5}\) unit
- D \(5 \sqrt{2}\) unit
Answer & Solution
Correct Answer
(B) \(\frac{5}{\sqrt{2}}\) unit
Step-by-step Solution
Detailed explanation
Hint : \(\begin{aligned} & A P=\sqrt{15^2-5^2}=10 \sqrt{2} \\ & \Delta=\frac{1}{2} \cdot B C \cdot A P=50 \sqrt{2} \\ & s=\frac{15+15+10}{2}=20 \\ & \because r=\frac{\Delta}{s}=\frac{50 \sqrt{2}}{20}=\frac{5}{\sqrt{2}}\end{aligned}\)
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