TS EAMCET · Maths · Properties of Triangles
\(\mathrm{PQR}\) is an isosceles triangle with \(\mathrm{PQ}=\mathrm{PR}\). If the radius of the circum circle of \(\triangle \mathrm{PQR}\) is equal to the length of \(\mathrm{PQ}\), then \(\angle \mathrm{P}=\)
- A \(30^{\circ}\)
- B \(60^{\circ}\)
- C \(45^{\circ}\)
- D \(120^{\circ}\)
Answer & Solution
Correct Answer
(D) \(120^{\circ}\)
Step-by-step Solution
Detailed explanation
\( R_c=P Q=\dot{b}=c \) Using sine rule \( \begin{aligned} & \frac{P Q}{\sin R}=2 R_c=P Q \times 2 \\ & \sin R=\frac{1}{2}, R=30^{\circ} \\ & \because \angle Q=\angle R \Rightarrow Q=30^{\circ} \\ & \therefore P=120^{\circ} . \end{aligned} \)
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