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Mathematics · 2026 · 2 marks
CBSE 2026 · Region 4 · Set 1 · Q22
D is a point on the side BC of ABC such that ∠ CAB =∠ CDA. Show that CA^2= CB × CD.
D is a point on the side BC of $\displaystyle \triangle \mathrm{ABC}$ such that $\displaystyle \angle \mathrm{CAB}=\angle \mathrm{CDA}$. Show that $\displaystyle \mathrm{CA}^{2}=\mathrm{CB} \times \mathrm{CD}$.
Marking-scheme solution
\[\begin{aligned}
& \triangle \mathrm{ADC} \sim \triangle \mathrm{BAC} \\
& \Rightarrow \frac{\mathrm{DC}}{\mathrm{AC}}=\frac{\mathrm{AC}}{\mathrm{BC}} \\
& \Rightarrow \mathrm{AC}^{2}=\mathrm{DC} \times \mathrm{BC}^{\circ} \text { or } \mathrm{CA}^{2}=\mathrm{CB} \times \mathrm{CD}
\end{aligned}
\]
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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.