Question 124

O is the circumcentre of ΔABC, given ∠BAC = 85° and ∠BCA = 55°, find ∠OAC.

Solution

Since $$\angle$$BAC = 85°

=> $$\angle$$BOC = 2 * 85 = 170°

Similarly, $$\angle$$AOB = 2 * $$\angle$$BCA = 2*55 = 110°

=> $$\angle$$AOC = 360° - 170° - 110° = 80°

Since, OA & OC are radii, => OA = OC, => $$\angle$$OAC = $$\angle$$OCA

In $$\triangle$$AOC

=> $$\angle$$OAC = $$\angle$$OCA = $$\frac{1}{2}(180^{\circ} - 80^{\circ})$$

= $$\frac{100}{2} = 50^{\circ}$$

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