Chapter Exam

Chapter 9 MATHS : Circles — Online MCQ Test

Q: In a circle, a perpendicular drawn from the centre to a chord:

Answer: A. Bisects the chord — The perpendicular from the centre of a circle to a chord bisects the chord. This is a basic theorem in circles.

Q: Equal chords of a circle subtend equal angles at the:

Answer: A. Centre of the circle — Equal chords subtend equal angles at the centre. This property is used frequently in circle geometry.

Q: A chord of a circle is 10 cm long. If the perpendicular from the centre to the chord bisects it, what is the length of each half?

Answer: B. 5 cm — Since the perpendicular from the centre bisects the chord, the 10 cm chord is divided into two equal parts of 5 cm each.

Q: Which statement is NOT true about chords of a circle?

Answer: D. A chord always passes through the centre — Not every chord passes through the centre. Only a diameter is a chord that passes through the centre.

Q: Which of the following is sufficient to prove that two chords of a circle are equal?

Answer: A. Their distances from the centre are equal — Chords that are equidistant from the centre of a circle are equal. This gives a direct criterion for equality of chords.

MATHS · CLASS 9th · Andhra State Board

Practice Chapter 9 MATHS : Circles with a free chapter-wise online MCQ test for Andhra State Board CLASS 9th MATHS. This chapter covers: This chapter covers chords perpendiculars from centre equal chord properties arc subtended angles and cyclic quadrilaterals.. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter 9 MATHS : Circles — Important Questions & Answers (FAQ)

Frequently asked questions from Andhra State Board CLASS 9th MATHS — Chapter 9 MATHS : Circles, with answers and explanations. These are sample questions; the exam has its own separate question set.

In a circle, a perpendicular drawn from the centre to a chord:

A. Bisects the chord ✓
B. Makes the chord equal to the radius
C. Bisects the arc only
D. Is always greater than the radius

Answer: A. Bisects the chord
The perpendicular from the centre of a circle to a chord bisects the chord. This is a basic theorem in circles.

Equal chords of a circle subtend equal angles at the:

A. Centre of the circle ✓
B. Chord itself
C. Diameter only
D. Tangent point

Answer: A. Centre of the circle
Equal chords subtend equal angles at the centre. This property is used frequently in circle geometry.

A chord of a circle is 10 cm long. If the perpendicular from the centre to the chord bisects it, what is the length of each half?

A. 2 cm
B. 5 cm ✓
C. 10 cm
D. 20 cm

Answer: B. 5 cm
Since the perpendicular from the centre bisects the chord, the 10 cm chord is divided into two equal parts of 5 cm each.

Which statement is NOT true about chords of a circle?

A. Equal chords subtend equal angles at the centre
B. Perpendicular from the centre to a chord bisects it
C. The longest chord of a circle is its diameter
D. A chord always passes through the centre ✓

Answer: D. A chord always passes through the centre
Not every chord passes through the centre. Only a diameter is a chord that passes through the centre.

Which of the following is sufficient to prove that two chords of a circle are equal?

A. Their distances from the centre are equal ✓
B. Their arcs are in the same circle
C. They subtend angles of 45° and 60° at the circumference
D. They are both less than the diameter

Answer: A. Their distances from the centre are equal
Chords that are equidistant from the centre of a circle are equal. This gives a direct criterion for equality of chords.