Question:
In the figure below, AB and AC are two tangents of the circle from the same external point A touching at points B and C, respectively. If ∠BAC = 2z° and ∠BDC = 5z°, then find the value of ∠BOC + ∠BAC in degrees.
In the figure below, AB and AC are two tangents of the circle from the same external point A touching at points B and C, respectively. If ∠BAC = 2z° and ∠BDC = 5z°, then find the value of ∠BOC + ∠BAC in degrees.
Updated On: Jul 29, 2024
- 105
- 135
- 140
- 155
- 160
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The Correct Option is B
Solution and Explanation
Join a line from B to C.
\(∠ABC = ∠BDC = 5z°\) [Alternate segment theorem]
Similarly, \(∠BCA = ∠CDB = 5z°\)
Thus, in \(△\;ABC\),
\(∠ABC + ∠BCA + ∠BAC = 180°\)
\(z = 15°\)
\(5z + 5z + 2z = 180°\)
So, \(∠BDC = 5(15) = 75°\)
Thus, \(∠BOC = 180° – 75° = 105°\) (As DBOC is a cyclic quadrilateral)
\(∠BAC = 2(15) = 30°\)
Hence, \(∠BOC + ∠BAC = 105° + 30° = 135°\)
Hence, option B is the correct answer.
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