Circles (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:
- Contact ✓ (correct)
- Intersection
- Origin
- Tangency
Q2. The angle subtended by an arc at the center is ____ the angle subtended at the circumference.
- Equal to
- Half of
- Twice ✓ (correct)
- Four times
Q3. A chord of a circle is:
- A line through the center
- A line touching the circle at one point
- A line segment joining two points on the circle ✓ (correct)
- The longest line in the circle
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 diameter
- The circumference
Q5. The circumference of a circle with radius r is:
- πr
- 2πr ✓ (correct)
- πr²
- 4πr
Q6. Two tangents drawn to a circle from an external point are:
- Perpendicular
- Parallel
- Equal in length ✓ (correct)
- Intersecting at 90°
Q7. The area of a circle with radius 7 cm is (use π = 22/7):
- 44 cm²
- 154 cm² ✓ (correct)
- 308 cm²
- 49 cm²
Q8. A semicircle subtends an angle of ____ at any point on the circumference.
- 45°
- 60°
- 90° ✓ (correct)
- 180°
Q9. If a line is tangent to a circle, it touches the circle at:
- Two points
- Three points
- Exactly one point ✓ (correct)
- No points
Q10. The angle in a semicircle is always:
- Acute
- Right ✓ (correct)
- Obtuse
- Straight
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 10 Mathematics MCQs
- Coordinate Geometry
- Arithmetic Progressions
- Circles
- Surface Areas and Volumes
- Trigonometry (Applications Case Study)
- Probability (Case Study)
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