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Mathematics

ABCD is a cyclic quadrilateral in a circle with centre O. If ∠ADC = 130°, find ∠BAC.

ABCD is a cyclic quadrilateral in a circle with centre O. If ∠ADC = 130°, find ∠BAC. Circles, Concise Mathematics Solutions ICSE Class 10.

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Answer

We know that,

Angle in a semi-circle is 90°.

∠ACB = 90°.

We know that,

Sum of opposite angles of a cyclic quadrilateral = 180°.

⇒ ∠ABC = 180° - ∠ADC = 180° - 130° = 50°.

In △ACB,

⇒ ∠ACB + ∠CBA + ∠BAC = 180° [Angle sum property]

⇒ 90° + 50° + ∠BAC = 180°

⇒ ∠BAC + 140° = 180°

⇒ ∠BAC = 180° - 140° = 40°.

Hence, ∠BAC = 40°.

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