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  • Write True or False and justify your answer in each of the following: If A, B, C and D are four points such that ∠BAC = 45° and ∠BDC = 45°, then A, B, C, D are concyclic.

Write True or False and justify your answer in each of the following: If A, B, C and D are four points such that \angle BAC=45^{\circ} and \angle BDC=45^{\circ}, then A, B, C, D are concyclic.

Answers (1)

True

Solution:

Definition of concyclic points: The points that lie on the same circle.

We know that angles in the same segment of a circle are equal

Since \angle BAC=45^{\circ}=\angle BDC

We know that these angles are in the same segment of a circle.

This can be represented as shown below:

BC is the chord of the circle and hence A, B, C & D are concyclic.

Therefore the given statement is true.

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infoexpert24

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