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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

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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…

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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:

  1. Contact ✓ (correct)
  2. Intersection
  3. Origin
  4. Tangency

Q2. The angle subtended by an arc at the center is ____ the angle subtended at the circumference.

  1. Equal to
  2. Half of
  3. Twice ✓ (correct)
  4. Four times

Q3. A chord of a circle is:

  1. A line through the center
  2. A line touching the circle at one point
  3. A line segment joining two points on the circle ✓ (correct)
  4. The longest line in the circle

Q4. If two chords intersect inside a circle, the product of their segments of one chord equals:

  1. The radius squared
  2. The product of segments of the other chord ✓ (correct)
  3. The diameter
  4. The circumference

Q5. The circumference of a circle with radius r is:

  1. πr
  2. 2πr ✓ (correct)
  3. πr²
  4. 4πr

Q6. Two tangents drawn to a circle from an external point are:

  1. Perpendicular
  2. Parallel
  3. Equal in length ✓ (correct)
  4. Intersecting at 90°

Q7. The area of a circle with radius 7 cm is (use π = 22/7):

  1. 44 cm²
  2. 154 cm² ✓ (correct)
  3. 308 cm²
  4. 49 cm²

Q8. A semicircle subtends an angle of ____ at any point on the circumference.

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

Q9. If a line is tangent to a circle, it touches the circle at:

  1. Two points
  2. Three points
  3. Exactly one point ✓ (correct)
  4. No points

Q10. The angle in a semicircle is always:

  1. Acute
  2. Right ✓ (correct)
  3. Obtuse
  4. 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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