Question

In the center circle O the angle BOA = 2ABD. How much does the angle measure BCA?

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Answer 1

`angleBCA=45^@`

Explanation:

let `angleABD=x, => angleBOA=2x`,
as `OA=OB, => angleOAB=angleOBA=x`,
consider `DeltaOAB, 4x=180, => x=45^@`,
recall that the angle at the center of a circle is twice the angle on the circumference subtended by the same arc,
and as `angleBOA and angleBCA` subtend the same arc `AB`,
`=> angleBCA=1/2angleBOA=x=45^@`