Question

In a circle with Centre C, take points P and Q on the circle such that PQ=radius of the circle.Measure angle PCQ. Is the triangle PCQ an equiangular triangle?

Answer 1

Answer:

R.E.F image

In OPSQ

∠0+∠P+∠S+∠Q=360

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⇒∠O+90

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+20

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+90

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=360

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⇒∠O=160

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Angle subtended by PQ at center is twice

that of subtended at circumference

⇒∠O=2∠PMQ

⇒160

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=2∠PMQ

⇒∠PMQ=80

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In PMQR, Sum of opposite angles =180

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(PMQR is cyclic)

⇒∠M+∠R=180

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⇒80

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+∠R=180

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⇒∠R=100

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