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.
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).
2. How many circles can pass through three points which are not collinear?
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 10.6, 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
Sanfoundry Global Education & Learning Series – Mathematics – Class 9.
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