Concyclic Points
Points are called concyclic if they lie on the same circle. Four points can often be tested for concyclicity by checking whether a pair of opposite angles is supplementary.
Practice This ConceptMain explanation
Teacher explanation
For three non-collinear points, a circle can always be drawn. For four points, the fourth point must also lie on that same circle. In Class 9 problems, opposite angles adding to 180 degrees is a common test.
Example
If in quadrilateral ABCD, angle A + angle C = 180 degrees, then A, B, C and D are concyclic.
Simple analogy
Four on one circle: opposite angles total 180.
Common confusion
Students may say any four points are concyclic. This is not true; the fourth point must satisfy the circle condition.
Exam tip
To prove four points concyclic, try to form a quadrilateral and check one pair of opposite angles.
Answer writing and exam use
1-mark use
Write the exact meaning of concyclic points in one clean line.
2-mark use
Define concyclic points and add one example or condition.
3-mark use
Explain concyclic points, show the method or example, and mention the common mistake.
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