ProofModerate2 marks

11(c)

In the given figure, ABCDE is a pentagon inscribed in a circle such that AC is a diameter and side BC||AE. If ∠BAC = 50°, find giving reasons:

∠BEC Hence, prove that BE is also a diameter.

Topic: Circle theorems

Previous-year question practice database

Answer

Exam answer

∠BEC = ∠BAC = 50° (same chord BC).

Also: ∠EBC = ∠EAC = 40° (same chord EC).

In ΔBEC: ∠BCE = 180°−50°−40° =90°.

Since chord BE subtends a 90° angle at C, BE is a diameter.

Answer: ∠BEC=50°; hence BE is a diameter.

Explanation

Angles in the same segment are equal. The converse of the angle-in-a-semicircle theorem proves BE is a diameter.