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Mathematics · 2024 · 2 marks
CBSE 2024 · Region 5 · Set 1 · Q21
If two tangents inclined at an angle of $\displaystyle 60$° are drawn to a circle of radius $\displaystyle 3$ cm, then find the length of each tangent.Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
If two tangents inclined at an angle of $\displaystyle 60$° are drawn to a circle of radius $\displaystyle 3$ cm, then find the length of each tangent.
Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
Marking-scheme solution
\(\displaystyle \angle \mathrm{APO}=30^{0}\)
\(\displaystyle \tan 30^{0}=\frac{1}{\sqrt{3}}=\frac{3}{A P}\)
\(\displaystyle \mathrm{AP}=3 \sqrt{3} \mathrm{~cm}\)
\[\angle \mathrm{OAY}=\angle \mathrm{OBP}=90^{\circ}
\]
But they are forming alternate interior angles
Therefore, PQ \(\displaystyle \| \mathrm{XY}\)
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CBSE Class 10 Mathematics past-paper question from the 2024board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.