CBSE 2025 · Region 1 · Set 1 · Q25 · 2 marks
A person is standing at P outside a circular ground at a distance of $\displaystyle 26$ m from the centre of the ground. He found that his distances from the points A and B on the ground are $\displaystyle 10$ m (PA and PB are tangents to the circle). Find the radius of the circular ground.
Marking-scheme solution
\(\displaystyle \angle \mathrm{OAP}=90^{\circ}\)
In right \(\displaystyle \Delta \mathrm{OAP}\),
\[\begin{aligned}
& (26)^{2}=\mathrm{OA}^{2}+(10)^{2} \\
\Rightarrow & \mathrm{OA}=\sqrt{576}=24 \\
\therefore & \text { radius }=24 \mathrm{~m}
\end{aligned}
\]
CirclesLength of Tangents from an External PointApplyvery_short_answermedium
More from Circles
- Which of the following statements is false?2025 · asked 3×
- At point A on the diameter AB of a circle of radius 10 cm, tangent XAY is drawn to the circle. Find the…2025 · asked 3×
- In the adjoining figure, XY and X'Y' are parallel tangents to a circle with centre O. Another tangent AB…2025 · asked 3×
- In the adjoining figure, PA and PB are tangents to a circle with centre O. The measure of angle APB is2025 · asked 3×
- In the given figure, RS is the tangent to the circle at the point L and MN is the diameter. If ∠ NML=30^°,…2025 · asked 3×
- Rectangle ABCD circumscribes the circle of radius 10 cm. Prove that ABCD is a square. Hence, find the…2025 · asked 3×
- In the given figure, PA is a tangent from an external point P to a circle with centre O. If ∠ POB=115^°, then…2025 · asked 3×
- In the given figure, O is the centre of the circle and BCD is tangent to it at C. Prove that ∠ BAC+∠…2025 · asked 3×
CBSE Class 10 Mathematics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.