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Circles (10 Mathematics)

A circle is a fundamental geometric shape with unique properties. Understanding circles helps solve problems related to tangents, chords, and angles.

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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 Jul 23, 2026

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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?

  1. They are parallel
  2. They are perpendicular ✓ (correct)
  3. They are equal
  4. They are complementary

Q2. How many tangents can be drawn from an external point to a circle?

  1. 1
  2. 2 ✓ (correct)
  3. 3
  4. Infinite

Q3. What is a secant to a circle?

  1. A line touching circle at one point
  2. A line intersecting circle at two points ✓ (correct)
  3. A line parallel to radius
  4. A line inside circle

Q4. What is the angle subtended by a diameter at any point on the circle?

  1. 45 degrees
  2. 60 degrees
  3. 90 degrees ✓ (correct)
  4. 180 degrees

Q5. What is the relationship between inscribed angle and central angle subtending the same arc?

  1. They are equal
  2. Inscribed angle is half of central angle ✓ (correct)
  3. Central angle is half of inscribed angle
  4. They sum to 180 degrees

Q6. What is the power of a point theorem?

  1. Two chords intersect
  2. If two chords intersect inside circle, then PA*PB = PC*PD ✓ (correct)
  3. Tangent equals chord
  4. Radius equals diameter

Q7. What is the circumference of a circle with radius r?

  1. πr^2
  2. 2πr ✓ (correct)
  3. πr
  4. πd

Q8. What is the area of a circle with radius r?

  1. 2πr
  2. πr^2 ✓ (correct)
  3. πr
  4. πr^2/2

Q9. What are the lengths of two tangents drawn from an external point?

  1. Different
  2. Equal ✓ (correct)
  3. Sum to radius
  4. Product equals radius

Q10. What is the angle between a tangent and a chord at point of contact?

  1. Equals inscribed angle in alternate segment ✓ (correct)
  2. Equals 90 degrees
  3. Equals central angle
  4. 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.

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