Circles (Class 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.
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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?
- They are perpendicular ✓ (correct)
- They are complementary
- They are parallel
- They are equal
Explanation: A tangent to a circle is perpendicular to the radius at the point of contact.
Q2. How many tangents can be drawn from an external point to a circle?
- 3
- 2 ✓ (correct)
- Infinite
- 1
Explanation: Exactly 2 tangents can be drawn from an external point to a circle, and they are equal in length.
Q3. What is a secant to a circle?
- A line touching circle at one point
- A line inside circle
- A line intersecting circle at two points ✓ (correct)
- A line parallel to radius
Explanation: A secant is a line that intersects a circle at two distinct points.
Q4. What is the angle subtended by a diameter at any point on the circle?
- 180 degrees
- 45 degrees
- 60 degrees
- 90 degrees ✓ (correct)
Explanation: By Thales' theorem, angle subtended by diameter at any point on the circle is 90 degrees.
Q5. What is the relationship between inscribed angle and central angle subtending the same arc?
- Inscribed angle is half of central angle ✓ (correct)
- They are equal
- They sum to 180 degrees
- Central angle is half of inscribed angle
Explanation: The inscribed angle is half the central angle when both subtend the same arc.
Q6. What is the power of a point theorem?
- Two chords intersect
- If two chords intersect inside circle, then PA*PB = PC*PD ✓ (correct)
- Radius equals diameter
- Tangent equals chord
Explanation: If two chords AB and CD intersect at point P inside a circle, then PA*PB = PC*PD.
Q7. What is the circumference of a circle with radius r?
- πr^2
- πr
- 2πr ✓ (correct)
- πd
Explanation: The circumference formula is C = 2πr, where r is the radius.
Q8. What is the area of a circle with radius r?
- πr
- πr^2/2
- 2πr
- πr^2 ✓ (correct)
Explanation: The area of a circle is A = πr^2.
Q9. 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.
Q10. What is the angle between a tangent and a chord at point of contact?
- Equals 90 degrees
- Equals inscribed angle in alternate segment ✓ (correct)
- Random
- Equals central angle
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 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 Class 10 Mathematics MCQs
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