Class 10 Maths MCQs on Tangent-Radius Perpendicular Property
Class 10 Maths MCQs on Tangent–Radius Perpendicular Property
Class: 10 | Subject: Mathematics
Chapter 10: Circles
Board: CBSE Board Examination (Strictly Based on Latest NCERT Curriculum)
1. The tangent at any point of a circle is perpendicular to the radius at the:
Correct Answer: B. Point of contact
Explanation: The fundamental theorem states that the tangent drawn at any point of a circle is perpendicular to the radius at the point where it touches the circle.
Explanation: The fundamental theorem states that the tangent drawn at any point of a circle is perpendicular to the radius at the point where it touches the circle.
2. If the radius makes an angle of 90° with a line at the point on the circle, the line is:
Correct Answer: C. Tangent
Explanation: A line perpendicular to the radius at its endpoint on the circle is a tangent.
Explanation: A line perpendicular to the radius at its endpoint on the circle is a tangent.
3. If the angle between the radius and a line at the point of contact is 90°, the line touches the circle at:
Correct Answer: B. One point
Explanation: A tangent touches the circle at exactly one point.
Explanation: A tangent touches the circle at exactly one point.
4. The angle between tangent and radius at the point of contact is always:
Correct Answer: C. 90°
Explanation: By theorem, the radius is perpendicular to the tangent at the point of contact.
Explanation: By theorem, the radius is perpendicular to the tangent at the point of contact.
5. If a line intersects the radius at an angle other than 90° at a point on the circle, it is:
Correct Answer: B. Secant
Explanation: Only when the angle is 90° is the line a tangent; otherwise, it cuts the circle at two points (secant).
Explanation: Only when the angle is 90° is the line a tangent; otherwise, it cuts the circle at two points (secant).
6. If radius = 7 cm, what is the angle between radius and tangent?
Correct Answer: C. 90°
Explanation: The angle is always 90°, independent of radius length.
Explanation: The angle is always 90°, independent of radius length.
7. A tangent and radius form a right triangle because they are:
Correct: C. Perpendicular
Explanation: The tangent is perpendicular to the radius.
Explanation: The tangent is perpendicular to the radius.
8. If a line touches the circle at two points, it cannot be:
Correct: B. Tangent
Explanation: Tangent touches at only one point.
Explanation: Tangent touches at only one point.
9. The perpendicular drawn from the centre to a tangent passes through:
Correct: C. Point of contact
Explanation: Radius meets tangent at point of contact forming 90°.
Explanation: Radius meets tangent at point of contact forming 90°.
10. If angle between radius and line is 90°, number of common points is:
Correct: B. 1
Explanation: That line is tangent touching at one point.
Explanation: That line is tangent touching at one point.
11. A tangent is drawn at point P. Radius OP is:
Correct: B. Perpendicular to tangent
Explanation: Fundamental property.
Explanation: Fundamental property.
12. If radius makes 90° with line, the line is unique because:
Correct: A. Only one perpendicular possible
Explanation: Through a point, only one perpendicular to a given line exists.
Explanation: Through a point, only one perpendicular to a given line exists.
13. Tangent lies in which plane relative to radius?
Correct: A. Same plane
Explanation: Both lie in same plane of circle.
Explanation: Both lie in same plane of circle.
14. If line forms 90° at point outside circle, it is:
Correct: B. Not tangent
Explanation: 90° must be at point on circle.
Explanation: 90° must be at point on circle.
15. Tangent is perpendicular to radius at:
Correct: C. Point of contact only
Explanation: Property valid only at touching point.
Explanation: Property valid only at touching point.
16. If tangent intersects circle again, it becomes:
Correct: B. Secant
Explanation: Then it cuts at two points.
Explanation: Then it cuts at two points.
17. Angle between tangent and chord at point of contact relates to:
Correct: A. Alternate segment theorem
Explanation: Another important circle property.
Explanation: Another important circle property.
18. If radius is extended beyond circle, perpendicular line there is:
Correct: B. Not tangent
Explanation: Must touch circle at that exact point.
Explanation: Must touch circle at that exact point.
19. Radius and tangent always form:
Correct: C. Right angle
Explanation: Always 90°.
Explanation: Always 90°.
20. Which theorem justifies perpendicular relation?
Correct: B. Tangent-Radius Theorem
Explanation: States tangent at any point of circle is perpendicular to radius at point of contact.
Explanation: States tangent at any point of circle is perpendicular to radius at point of contact.