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Mathematics

In the given figure, ∠ABC and ∠DBC are inscribed in a circle such that ∠BAC = 60° and ∠DBC = 40°. Then, ∠BCD = ?

  1. 60°

  2. 40°

  3. 100°

  4. 80°

In the given figure, ∠ABC and ∠DBC are inscribed in a circle such that ∠BAC = 60° and ∠DBC = 40°. Loci, RSA Mathematics Solutions ICSE Class 10.

Circles

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Answer

Given,

Points A and D are on the circle, and both form angles with the chord BC.

∠BDC = ∠BAC = 60° [Angles in same segment are equal]

In ΔBCD,

By angle sum property of triangle,

∠BCD + ∠DBC + ∠BDC = 180°

∠BCD = 180° - ∠DBC - ∠BDC

∠BCD = 180° - 40° - 60°

∠BCD = 80°.

Hence, option 4 is the correct option.

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