Question 173

O is the circumcentre of the triangle ABC and ∠BAC = 85°, ∠BCA = 75°, then the value of ∠OAC is

Solution

$$\angle$$BAC = 85°

$$\angle$$BCA = 75°

=> $$\angle$$ABC = 180°-(85°+75°) = 20°

Angle subtended by an arc at the centre is twice the angle subtended by it at any point on the circle.

=> $$\angle$$AOC = 2$$\angle$$ABC

=> $$\angle$$AOC = 40°

In $$\triangle$$OAC, OA = OC = radii

=> $$\angle$$OAC = $$\angle$$OCA

=> 2$$\angle$$OAC = 180°-40° = 140°

=> $$\angle$$OAC = $$\frac{140^{\circ}}{2}$$ = 70°

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