Question

In the given figure, O is the centre of the circle and BA = AC. If ∠ABC = 50o, find ∠BOC and ∠BDC.

Answer 1

Answer:

The measure of ∠BOC is 160° and ∠BDC is 80°.

Step-by-step explanation:

It is given that BA = AC, it means triangle ABC is an isosceles triangle. The two angles inclined on equal and non equal lines are same.

$\angle ABC=\angle ACB=50^{\circ}$

Using the angle sum property of triangle,

$\angle ABC+\angle ACB+\angle BAC=180^{\circ}$

$50^{\circ}+50^{\circ}+\angle BAC=180^{\circ}$

$100^{\circ}+\angle BAC=180^{\circ}$

$\angle BAC=80^{\circ}$

According to the central angle theorem, the central angle from any two points on the circle is always twice the inscribed angle from those two points.

$\angle BOC=2\times \angle BAC$

$\angle BOC=2\times 80^{\circ}$

$\angle BOC=160^{\circ}$

Using central angle theorem,

$\angle BOC=2\times \angle BDC$

$160^{\circ}=2\times \angle BDC$

$\angle BDC=80^{\circ}$

Therefore the measure of ∠BOC is 160° and ∠BDC is 80°.

Answer 2

Answer:

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Step-by-step explanation:

angle BOC =160 degree and angle BDC = 80 degree