Chapter 9: Tangents and Secants to a Circle — Online MCQ Test
MATHS · CLASS 10th · Telangana State Board
Practice Chapter 9: Tangents and Secants to a Circle with a free chapter-wise online MCQ test.
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.
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Chapter 9: Tangents and Secants to a Circle — Important Questions & Answers
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.
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°.
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.
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.
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).
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).