Question
Download Solution PDFAn equilateral triangle ABC is inscribed in a circle with centre O. D is a point on the minor arc BC and ∠CBD = 40º. Find the measure of ∠BCD.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
An equilateral triangle ABC is inscribed in a circle with centre O
∠CBD = 40º
Concept used:
The sum of the opposite angles of a cyclic quadrilateral = 180°
The sum of all three angles of a triangle = 180°
Calculation:
∠ABC = ∠ACB = ∠BAC = 60° [∵ ΔABC is an equilateral triangle]
Also, ∠BAC + ∠BDC = 180°
⇒ 60° + ∠BDC = 180°
⇒ ∠BDC = 180° - 60° = 120°
Also, ∠CBD + ∠BDC + ∠BCD = 180°
⇒ 40° + 120° + ∠BCD = 180°
⇒ ∠BCD = 180° - 40° - 120° = 20°
∴ The value of ∠BCD is 20°
Last updated on Jul 17, 2025
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