Circles (10 Mathematics)
A circle is a fundamental geometric shape with unique properties. Understanding circles helps solve problems related to tangents, chords, and angles.
TL;DR: A circle is a fundamental geometric shape with unique properties. Understanding circles helps solve problems related to tangents, chords, and angles.
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
A circle is a fundamental geometric shape with unique properties. Understanding circles helps solve problems related to tangents, chords, and angles.
Circles MCQs with Answers & Explanations
Q1. What is the relationship between a tangent and radius at the point of contact?
- They are parallel
- They are perpendicular ✓ (correct)
- They are equal
- They are complementary
Q2. How many tangents can be drawn from an external point to a circle?
- 1
- 2 ✓ (correct)
- 3
- Infinite
Q3. What is a secant to a circle?
- A line touching circle at one point
- A line intersecting circle at two points ✓ (correct)
- A line parallel to radius
- A line inside circle
Q4. What is the angle subtended by a diameter at any point on the circle?
- 45 degrees
- 60 degrees
- 90 degrees ✓ (correct)
- 180 degrees
Q5. What is the relationship between inscribed angle and central angle subtending the same arc?
- They are equal
- Inscribed angle is half of central angle ✓ (correct)
- Central angle is half of inscribed angle
- They sum to 180 degrees
Q6. 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
Q7. What is the circumference of a circle with radius r?
- πr^2
- 2πr ✓ (correct)
- πr
- πd
Q8. What is the area of a circle with radius r?
- 2πr
- πr^2 ✓ (correct)
- πr
- πr^2/2
Q9. What are the lengths of two tangents drawn from an external point?
- Different
- Equal ✓ (correct)
- Sum to radius
- Product equals radius
Q10. What is the angle between a tangent and a chord at point of contact?
- Equals inscribed angle in alternate segment ✓ (correct)
- Equals 90 degrees
- Equals central angle
- Random
Frequently Asked Questions
What is the difference between a chord and a secant?
A chord is a line segment with both endpoints on the circle. A secant is a line that intersects the circle at two points. The chord is part of the secant.
How do you find the length of a chord given the radius and distance from center?
Use the formula: chord length = 2√(r^2 - d^2), where r is radius and d is perpendicular distance from center to chord.
More 10 Mathematics MCQs
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- Probability (Case Study)
- Coordinate Geometry (Case Study)
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