Chapter Exam

Chapter 9: Tangents and Secants to a Circle — Online MCQ Test

Q: A tangent to a circle is a line that touches the circle at exactly _____ point(s).

Answer: A. one — By definition, a tangent is a line that intersects a circle at exactly one point, called the point of contact or point of tangency.

Q: The angle between a tangent and the radius at the point of contact is:

Answer: C. 90° — A fundamental theorem states that the tangent to a circle is perpendicular to the radius at the point of contact, making the angle 90°.

Q: From an external point P, two tangents are drawn to a circle with center O. If the tangents touch the circle at points A and B, then PA is _____ to PB.

Answer: C. equal — The lengths of tangents drawn from an external point to a circle are equal. Therefore, PA = PB.

Q: From an external point P, a tangent PA and a secant PBC are drawn to a circle (where B and C are on the circle). The relationship PA² = PB × PC represents:

Answer: D. Both (a) and (b) — The Power of a Point Theorem states that for a tangent and secant from the same external point, PA² = PB × PC. This is also known as the Tangent-Secant Theorem.

Q: A circle has radius r. From an external point at distance d from the center (d > r), a tangent is drawn. The length of the tangent is:

Answer: C. √(d² - r²) — If P is the external point, O is the center, and A is the point of tangency, triangle OAP is right-angled at A. By Pythagoras: PA² = PO² - OA² = d² - r², so PA = √(d² - r²).

MATHS · CLASS 10th · Telangana State Board

Practice Chapter 9: Tangents and Secants to a Circle with a free chapter-wise online MCQ test for Telangana State Board CLASS 10th MATHS. This chapter covers: This chapter investigates lines intersecting or touching a circle. Students prove that a tangent is perpendicular to the radius at the point of contact. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter 9: Tangents and Secants to a Circle — Important Questions & Answers (FAQ)

Frequently asked questions from Telangana State Board CLASS 10th MATHS — Chapter 9: Tangents and Secants to a Circle, with answers and explanations. These are sample questions; the exam has its own separate question set.

A tangent to a circle is a line that touches the circle at exactly _____ point(s).

A. one ✓
B. two
C. three
D. infinite

Answer: A. one
By definition, a tangent is a line that intersects a circle at exactly one point, called the point of contact or point of tangency.

The angle between a tangent and the radius at the point of contact is:

A. 45°
B. 60°
C. 90° ✓
D. 180°

Answer: C. 90°
A fundamental theorem states that the tangent to a circle is perpendicular to the radius at the point of contact, making the angle 90°.

From an external point P, two tangents are drawn to a circle with center O. If the tangents touch the circle at points A and B, then PA is _____ to PB.

A. greater than
B. less than
C. equal ✓
D. perpendicular

Answer: C. equal
The lengths of tangents drawn from an external point to a circle are equal. Therefore, PA = PB.

From an external point P, a tangent PA and a secant PBC are drawn to a circle (where B and C are on the circle). The relationship PA² = PB × PC represents:

A. Tangent-Secant Theorem
B. Power of a Point Theorem
C. Pythagorean Theorem
D. Both (a) and (b) ✓

Answer: D. Both (a) and (b)
The Power of a Point Theorem states that for a tangent and secant from the same external point, PA² = PB × PC. This is also known as the Tangent-Secant Theorem.

A circle has radius r. From an external point at distance d from the center (d > r), a tangent is drawn. The length of the tangent is:

A. d
B. √(d² + r²)
C. √(d² - r²) ✓
D. d - r

Answer: C. √(d² - r²)
If P is the external point, O is the center, and A is the point of tangency, triangle OAP is right-angled at A. By Pythagoras: PA² = PO² - OA² = d² - r², so PA = √(d² - r²).

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