Asked in: March 2024 board paper (same Apollonius type in June 2026)Seg PM is a median of \(\Delta PQR\), PM = 9 and \(PQ^2 + PR^2 = 290\), then find QR.

Doubtly Asked 29 Oct 2026 Practice test ssc 10th Save WhatsApp Report

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Answer: QR = 16

In \(\Delta PQR\), seg PM is a median, so M is the midpoint of QR.

By Apollonius theorem, \(PQ^2 + PR^2 = 2PM^2 + 2QM^2\).

\(290 = 2 \times 9^2 + 2QM^2 = 162 + 2QM^2\) \(\therefore 2QM^2 = 128\) \(\therefore QM^2 = 64\) \(\therefore QM = 8\).

\(QR = 2 \times QM = 2 \times 8 = 16\).

Doubtly AI · 29 Oct 2026 AI-generated · not yet verified Report

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