This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Circles through Three Points”.

1. If a circle passes through three points which are collinear, the third point either lies outside or inside the circle.

a) True

b) False

View Answer

Answer: a

Explanation: As shown in diagrams below, if a circle passes through three collinear points A, B and C, the third point either lies outside the circle (figure 1) or inside the circle (figure 2).

Explanation: As shown in diagrams below, if a circle passes through three collinear points A, B and C, the third point either lies outside the circle (figure 1) or inside the circle (figure 2).

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2. How many circles can pass through three points which are not collinear?

a) One

b) Two

c) Three

d) Four

View Answer

Answer: a

Explanation: According to theorem 10.5, there is one and only one circle passing through three given non-collinear points.

As can be seen in the diagram below, there can be only one circle through three non-collinear points A,B and C.

Explanation: According to theorem 10.5, there is one and only one circle passing through three given non-collinear points.

As can be seen in the diagram below, there can be only one circle through three non-collinear points A,B and C.

3. From the diagram given below, if for two chords AB and CD, AB = CD, which of the following is true?

a) OM < ON

b) OM > ON

c) OM = ON

d) OM ≠ ON

View Answer

Answer: c

Explanation: According to theorem 10.6, equal chords of a circle are equidistant from the centre.

OM and on are the distance from the centre and chords AB = CD (given).

Hence, OM = ON

Explanation: According to theorem 10.6, equal chords of a circle are equidistant from the centre.

OM and on are the distance from the centre and chords AB = CD (given).

Hence, OM = ON

Check this: Class 8 Mathematics MCQs | Class 9 - Mathematics Books

**Sanfoundry Global Education & Learning Series – Mathematics – Class 9**.

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