Question : In $\triangle PQR, PQ=QR$ and $O$ is an interior point of $\triangle PQR$ such that $\angle OPR=\angle ORP$.
Consider the following statements:
(i) $\triangle POR$ is an isosceles triangle.
(ii) $O$ is the centroid of $\triangle PQR$.
(iii) $\triangle PQO$ is congruent to $\triangle RQO$.
Which of the above statements is/are correct?
Option 1: Only (i) and (ii)
Option 2: Only (i) and (iii)
Option 3: Only (ii) and (iii)
Option 4: Only (ii)
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
Correct Answer: Only (i) and (iii)
Solution :
Given: In $\triangle PQR, PQ=QR$ and $O$ is an interior point of $\triangle PQR$ such that $\angle OPR=\angle ORP$.
Since $PQ = QR$, so $\triangle PQR$ is an isosceles triangle.
From the given data we cannot say that $O$ is the centroid of the $\triangle PQR$.
Also, $PQ=QR, OP=OR$ and $OQ=OQ$
So, $\triangle PQO$ and $\triangle RQO$ are congruent.
Hence, the correct answer is Only (i) and (iii).
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Get Updates Brochure
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
