Question

A circle with centre P.
arc AB = arc BC and
arc AXC = 2 arc AB.
Find measure of
arc AB, arc BC and
arc AXC. Prove chord
AB congruent chord BC​

Answer 1

Step-by-step explanation:

We know that the arc of equal lengths subtend equal angles at the centre.

hence ∠AOB=∠BOC=48

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Then ∠AOC=∠AOB+∠BOC=48

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+48

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=96

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The triangle thus formed, △BOC is an isosceles triangle with OB=OC as they are radii of the same circle.

Thus ∠BOC=∠OCB as they are opposite angles of equal sides of an isosceles triangle.

The sum of all the angels of a triangle is 180

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so, ∠BOC+∠OBC+∠OCB=180

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2∠OBC+48

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=180

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as ∠OBC=∠OCB

2∠OBC=180

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−48

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2∠OBC=132

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∠OBC=66

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as ∠OBC=∠OCB

So, ∠OBC=∠OCB=66

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Answer 2

I hope this is correct and this help you