Chapter Exam

Chapter 10: Circles — Online MCQ Test

Q: A line that touches a circle at exactly one point is called a:

Answer: B. Tangent — A tangent to a circle touches it at exactly one point, called the point of contact.

Q: The radius drawn to the point of contact of a tangent is:

Answer: B. Perpendicular to the tangent — According to the tangent-radius theorem, the radius through the point of contact is perpendicular to the tangent.

Q: From an external point P, a tangent PA is drawn to a circle with centre O. If OP = 13 cm and OA = 5 cm, then PA is:

Answer: C. 12 cm — Since OA is perpendicular to PA, triangle OAP is right-angled. PA = √(13² - 5²) = √144 = 12 cm.

Q: Tangents PA and PB are drawn from P to a circle with centre O. If ∠APB = 80°, then ∠OAB is:

Answer: A. 40° — Here ∠AOB = 180° - 80° = 100°. In isosceles triangle AOB, ∠OAB = (180° - 100°)/2 = 40°.

Q: From point P, tangents PA and PB are drawn to a circle with centre O. If ∠APB = 2x + 20° and ∠AOB = 3x + 10°, then x is:

Answer: B. 30° — The angles ∠APB and ∠AOB are supplementary, so (2x + 20) + (3x + 10) = 180. This gives x = 30°.

MATHS · CLASS 10th · Karnataka State Board

Practice Chapter 10: Circles with a free chapter-wise online MCQ test for Karnataka State Board CLASS 10th MATHS. This chapter covers: Tangent Secant Radius Point of contact Number of tangents Equal tangents Tangent properties Circle theorems. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter 10: Circles — Important Questions & Answers (FAQ)

Frequently asked questions from Karnataka State Board CLASS 10th MATHS — Chapter 10: Circles, with answers and explanations. These are sample questions; the exam has its own separate question set.

A line that touches a circle at exactly one point is called a:

A. Secant
B. Tangent ✓
C. Chord
D. Diameter

Answer: B. Tangent
A tangent to a circle touches it at exactly one point, called the point of contact.

The radius drawn to the point of contact of a tangent is:

A. Parallel to the tangent
B. Perpendicular to the tangent ✓
C. Equal to the tangent
D. A secant of the circle

Answer: B. Perpendicular to the tangent
According to the tangent-radius theorem, the radius through the point of contact is perpendicular to the tangent.

From an external point P, a tangent PA is drawn to a circle with centre O. If OP = 13 cm and OA = 5 cm, then PA is:

A. 8 cm
B. 10 cm
C. 12 cm ✓
D. 18 cm

Answer: C. 12 cm
Since OA is perpendicular to PA, triangle OAP is right-angled. PA = √(13² - 5²) = √144 = 12 cm.

Tangents PA and PB are drawn from P to a circle with centre O. If ∠APB = 80°, then ∠OAB is:

A. 40° ✓
B. 50°
C. 80°
D. 100°

Answer: A. 40°
Here ∠AOB = 180° - 80° = 100°. In isosceles triangle AOB, ∠OAB = (180° - 100°)/2 = 40°.

From point P, tangents PA and PB are drawn to a circle with centre O. If ∠APB = 2x + 20° and ∠AOB = 3x + 10°, then x is:

A. 20°
B. 30° ✓
C. 40°
D. 50°

Answer: B. 30°
The angles ∠APB and ∠AOB are supplementary, so (2x + 20) + (3x + 10) = 180. This gives x = 30°.

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