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An 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.
  • a)
    40º
  • b)
    30º
  • c)
    50º
  • d)
    20º
  • e)
    10º
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
An equilateral triangle ABC is inscribed in a circle with centre O. D ...
∠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°
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Most Upvoted Answer
An equilateral triangle ABC is inscribed in a circle with centre O. D ...
∠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°
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Community Answer
An equilateral triangle ABC is inscribed in a circle with centre O. D ...
∠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°
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An 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.a)40ºb)30ºc)50ºd)20ºe)10ºCorrect answer is option 'D'. Can you explain this answer? for UCAT 2025 is part of UCAT preparation. The Question and answers have been prepared according to the UCAT exam syllabus. Information about An 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.a)40ºb)30ºc)50ºd)20ºe)10ºCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for UCAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An 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.a)40ºb)30ºc)50ºd)20ºe)10ºCorrect answer is option 'D'. Can you explain this answer?.
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