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Class 10 Circles worksheet
CBSE Mathematics. Tangents: at right angles to the radius, equal from an outside point. Every sheet has 20 questions in three sections and an answer key, and the numbers change every time.
Sample questions
Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.
Section A · multiple choice
- 1.
From a point P, 26 cm from the centre O of a circle of radius 24 cm, a tangent PQ is drawn. The length of PQ is:
- 50 cm
- 2 cm
- 11 cm
- 10 cm
Answer
(d) 10 cm
OQ ⟂ PQ, so PQ = √(26² − 24²) = 10
- 2.
The tangent from a point P to a circle of radius 24 cm is 18 cm long. The distance of P from the centre is:
- 42 cm
- 6 cm
- 30 cm
- 31 cm
Answer
(c) 30 cm
OP = √(24² + 18²) = 30
- 3.
PA and PB are tangents from P to a circle with centre O. If ∠APB = 115°, then ∠AOB is:
- 245°
- 115°
- 32.5°
- 65°
Answer
(d) 65°
∠OAP = ∠OBP = 90°, so ∠AOB = 360° − 180° − 115° = 65°
Section B · short answer
- 4.
Find the length of the tangent drawn to a circle of radius 105 cm from a point 111 cm from its centre.
Answer
36 cm
√(111² − 105²) = √1296 = 36
- 5.
Tangents PA and PB are drawn from an external point P to a circle with centre O. If ∠AOB = 155°, find ∠APB.
Answer
25°
OAPB has two right angles, so ∠APB = 180° − 155° = 25°
Section C · long answer
- 6.
A circular park has a radius of 12 m. Isha stands 15 m from its centre and walks in a straight line that just touches the edge of the park. How far does Isha walk to reach the edge?
Answer
9 m
the path is a tangent, at right angles to the radius: √(15² − 12²) = 9
Fresh sheets for your child
In the app, every Circles sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.
Coming soon for Android and iPhone.