Circles through Three Points Questions and Answers

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).

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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.

maths-questions-answers-circles-through-three-points-q2

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

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