Circles (Class 10 Mathematics)
A circle is a locus of points equidistant from a center. Understanding properties like tangents, chords, arcs, and angles is fundamental to geometry and tr
TL;DR: A circle is a locus of points equidistant from a center. Understanding properties like tangents, chords, arcs, and angles is fundamental to geometry a…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
A circle is a locus of points equidistant from a center. Understanding properties like tangents, chords, arcs, and angles is fundamental to geometry and tr
Circles MCQs with Answers & Explanations
Q1. A tangent to a circle is perpendicular to the radius at the point of:
- Intersection
- Tangency
- Contact ✓ (correct)
- Origin
Explanation: At the point of contact, a tangent is perpendicular to the radius of the circle.
Q2. The angle subtended by an arc at the center is ____ the angle subtended at the circumference.
- Half of
- Equal to
- Four times
- Twice ✓ (correct)
Explanation: The angle subtended at the center is twice the angle subtended by the same arc at any point on the circumference.
Q3. A chord of a circle is:
- A line segment joining two points on the circle ✓ (correct)
- A line touching the circle at one point
- The longest line in the circle
- A line through the center
Explanation: A chord is a line segment with both endpoints on the circle. A diameter is a special chord passing through the center.
Q4. If two chords intersect inside a circle, the product of their segments of one chord equals:
- The radius squared
- The product of segments of the other chord ✓ (correct)
- The circumference
- The diameter
Explanation: The intersecting chords theorem states: if chords AB and CD intersect at P, then AP × PB = CP × PD.
Q5. The circumference of a circle with radius r is:
- 4πr
- πr²
- 2πr ✓ (correct)
- πr
Explanation: Circumference = 2πr, where r is the radius.
Q6. Two tangents drawn to a circle from an external point are:
- Perpendicular
- Parallel
- Intersecting at 90°
- Equal in length ✓ (correct)
Explanation: Tangents from an external point to a circle are equal in length and make equal angles with the line joining the point to the center.
Q7. The area of a circle with radius 7 cm is (use π = 22/7):
- 154 cm² ✓ (correct)
- 308 cm²
- 49 cm²
- 44 cm²
Explanation: Area = πr² = (22/7) × 7² = (22/7) × 49 = 22 × 7 = 154 cm².
Q8. A semicircle subtends an angle of ____ at any point on the circumference.
- 180°
- 90° ✓ (correct)
- 45°
- 60°
Explanation: By Thales' theorem, any angle inscribed in a semicircle (subtended by the diameter) is 90°.
Q9. If a line is tangent to a circle, it touches the circle at:
- No points
- Two points
- Exactly one point ✓ (correct)
- Three points
Explanation: A tangent line touches a circle at exactly one point and does not intersect it elsewhere.
Q10. The angle in a semicircle is always:
- Obtuse
- Acute
- Straight
- Right ✓ (correct)
Explanation: Any angle inscribed in a semicircle (with the diameter as one side) is always a right angle (90°).
Q11. What is the relationship between a tangent and radius at the point of contact?
- They are perpendicular ✓ (correct)
- They are complementary
- They are equal
- They are parallel
Explanation: A tangent to a circle is perpendicular to the radius at the point of contact.
Q12. How many tangents can be drawn from an external point to a circle?
- 1
- 2 ✓ (correct)
- 3
- Infinite
Explanation: Exactly 2 tangents can be drawn from an external point to a circle, and they are equal in length.
Q13. What is a secant to a circle?
- A line touching circle at one point
- A line parallel to radius
- A line intersecting circle at two points ✓ (correct)
- A line inside circle
Explanation: A secant is a line that intersects a circle at two distinct points.
Q14. What is the angle subtended by a diameter at any point on the circle?
- 60 degrees
- 180 degrees
- 45 degrees
- 90 degrees ✓ (correct)
Explanation: By Thales' theorem, angle subtended by diameter at any point on the circle is 90 degrees.
Q15. What is the relationship between inscribed angle and central angle subtending the same arc?
- Inscribed angle is half of central angle ✓ (correct)
- They sum to 180 degrees
- They are equal
- Central angle is half of inscribed angle
Explanation: The inscribed angle is half the central angle when both subtend the same arc.
Q16. What is the power of a point theorem?
- Two chords intersect
- If two chords intersect inside circle, then PA*PB = PC*PD ✓ (correct)
- Tangent equals chord
- Radius equals diameter
Explanation: If two chords AB and CD intersect at point P inside a circle, then PA*PB = PC*PD.
Q17. What is the circumference of a circle with radius r?
- πr
- πd
- 2πr ✓ (correct)
- πr^2
Explanation: The circumference formula is C = 2πr, where r is the radius.
Q18. What is the area of a circle with radius r?
- 2πr
- πr
- πr^2/2
- πr^2 ✓ (correct)
Explanation: The area of a circle is A = πr^2.
Q19. What are the lengths of two tangents drawn from an external point?
- Equal ✓ (correct)
- Sum to radius
- Different
- Product equals radius
Explanation: The two tangents drawn from an external point to a circle are equal in length.
Q20. What is the angle between a tangent and a chord at point of contact?
- Equals central angle
- Equals inscribed angle in alternate segment ✓ (correct)
- Equals 90 degrees
- Random
Explanation: By the alternate segment theorem, the angle between tangent and chord equals the inscribed angle in the alternate segment.
Frequently Asked Questions
What is the relationship between a chord and its perpendicular distance from the center?
The perpendicular from the center of a circle to a chord bisects the chord. Additionally, equal chords are equidistant from the center, and chords at different distances from the center have different lengths.
How can the power of a point be used to solve circle problems?
The power of a point is the product of distances from the point to the two intersection points of any line through it intersecting the circle. This is constant for a given point and helps solve problems involving tangents, secants, and chords.
More Class 10 Mathematics MCQs
🤖 Stuck on any of these? Ask Syllab's free AI Tutor to explain step by step →