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Mathematics · 2026 · 2 marks
CBSE 2026 · Region 3 · Set 2 · Q22
Two right triangles PRQ and PSQ are drawn on the same hypotenuse PQ. If PR and QS intersect at T, prove that ST × TQ = PT × TR.
Two right triangles PRQ and PSQ are drawn on the same hypotenuse PQ . If PR and QS intersect at T , prove that $\displaystyle \mathrm{ST} \times \mathrm{TQ}=\mathrm{PT} \times \mathrm{TR}$.
Marking-scheme solution
$\displaystyle \begin{array}{l}\Delta \mathrm{STP} \sim \Delta \mathrm{RTQ}
\frac{\mathrm{ST}}{\mathrm{TP}}=\frac{\mathrm{RT}}{\mathrm{TQ}} \Rightarrow \mathrm{ST} \times \mathrm{TQ}=\mathrm{PT} \times \mathrm{TR}\end{array}$
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CBSE Class 10 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.