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Mathematics · 2022 · 4 marks
CBSE 2022 · Region 1 · Set 1 · Q12
In Figure 1, a triangle ABC with ∠ B =90^° is shown. Taking AB as diameter, a circle has been drawn intersecting AC at point P. Prove that the…
In Figure $\displaystyle 1$, a triangle ABC with $\displaystyle \angle \mathrm{B}=90^{\circ}$ is shown. Taking AB as diameter, a circle has been drawn intersecting AC at point P. Prove that the tangent drawn at point P bisects BC.
Figure $\displaystyle 1$
Figure $\displaystyle 1$Marking-scheme solution
\[\mathrm{PR}=\mathrm{RB} \text { (tangents from external point). }
\]
Proving \(\displaystyle \angle \mathrm{RPC}=\angle \mathrm{RCP}\)
\[\Rightarrow \quad \text { PR }=\text { CR }
\]
Using equations (i) and (ii)
BR= RC
Hence the tangent drawn at point P bisects BCMore from Circles
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CBSE Class 10 Mathematics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.