Question

I want the answer with explanation ​

Answer 1

Angle ABC is equal to Angle BAC

So 50 = 2x + 20

2x = 30

X = 15 °

Answer 2

O is the center of the circle. If ∠BAC=50

∘

, find ∠OBC

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Medium

Solution

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Given a circle with it's center at O

∠BAC=50

∘

∠BOC=2∠BAC (Angle made by a chord at centre is twice of angle it makes with circumference.)

=2(50

∘

)

=100

∘

In △OBC,OB=OC=radius

⇒∠OBC=∠OCB ( opposite angles of equal sides of a △ )

Sum of angles in a triangle = 180

∘

∠OBC+∠OCB+∠BOC=180

∘

....(1)

Let∠OBC=∠OCB=x

⟹x+x+∠BOC=180

∘

From (1)

2x=180

∘

−100

∘

=80

∘

⟹x=40

∘

∴∠OBC=x=40

∘

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SIMILAR QUESTIONS

star-struck

Prove that the angle subtended at the centre of a circle is bisected by the radius passing through the mid-point of the arc.

Medium

Two chords AB and AC of a circle subtends angles equal to 90

o

and 150

o

, respectively at the centre. Find ∠BAC, if AB and AC lie on the opposite sides of the centre.