Chapter 10: Circles — Online MCQ Test
MATHS · CLASS 10th · Karnataka State Board
Practice Chapter 10: Circles with a free chapter-wise online MCQ test.
This chapter covers: Tangent Secant Radius Point of contact Number of tangents Equal tangents Tangent properties Circle theorems.
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Chapter 10: Circles — Important Questions & Answers
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.
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.
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.
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°.
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°.
The angles ∠APB and ∠AOB are supplementary, so (2x + 20) + (3x + 10) = 180. This gives x = 30°.