triangle abc is inscribed in a circle with centre o . if mangle BAC = 30° , then prove that triangle OBC is an equilateral triangle.
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△ABC is an equilateral triangle inscribed in a circle with center O.
⇒ ∠ABC=∠BCA=∠CAB=60
o
[ Angles of equilateral triangle ]
⇒ We know that, angle subtended at the center of a circle is double angle at any point on circumference of circle.
∴ ∠BOC=2∠CAB
∴ ∠BOC=2×60
o
∴ ∠BOC=120
o
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