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