✓ Board-verified
Mathematics · 2025 · 3 marks
CBSE 2025 · Region 3 · Set 1 · Q31
In the given figure, PC is a tangent to the circle at C. AOB is the diameter which when extended meets the tangent at P. Find ∠ CBA and ∠ BCO, if ∠…
In the given figure, PC is a tangent to the circle at C. AOB is the diameter which when extended meets the tangent at P. Find $\displaystyle \angle \mathrm{CBA}$ and $\displaystyle \angle \mathrm{BCO}$, if $\displaystyle \angle \mathrm{PCA}=110^{\circ}$.
Marking-scheme solution
\[\begin{aligned}
& \angle \mathrm{ACB}=\angle \mathrm{OCB}+\angle \mathrm{OCA}=90^{\circ} \\
& \angle \mathrm{PCB}+\angle \mathrm{OCB}+\angle \mathrm{OCA}=110^{\circ} \\
& \angle \mathrm{PCB}=110^{\circ}-90^{\circ}=20^{\circ} \\
& \angle \mathrm{PCB}+\angle \mathrm{OCB}=90^{\circ} \\
& \angle \mathrm{OCB}=90^{\circ}-20^{\circ}=70^{\circ} \\
& \mathrm{As} \mathrm{OB}=\mathrm{OC} \Rightarrow \angle \mathrm{OBC}=\angle \mathrm{OCB} \\
& \angle \mathrm{OBC}=\angle \mathrm{OCB}=70^{\circ}
\end{aligned}
\]
More from Circles
- In the given figure, TA is a tangent to the circle with centre O such that OT=4 cm, ∠ OTA=30^°, then length of TA is:2023
- Assertion: Radius is the smallest distance of a tangent from the centre of the circle. Reason (R): Radius is perpendicular to the tangent.2026
- Assertion: The tangents drawn at the end points of a diameter of a circle, are parallel. Reason (R): Diameter of a circle is the longest chord.2024
- Prove that the parallelogram circumscribing a circle is a rhombus.2024
- A backyard is in the shape of a triangle ABC with right angle at B. AB=7 m and BC=15 m. A circular pit was dug inside it such that it touches the…2024
- PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If OP=13 cm, then…2026
- In Fig. 1, AB is diameter of a circle centered at O. BC is tangent to the circle at B. If OP bisects the chord AD and ∠ AOP=60^°, then find m ∠ C.…2022
- PQ is tangent to a circle with centre O. If ∠ POR=65^°, then m ∠ PTR is2026
CBSE Class 10 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.