1. ## Circle geo question

How did I get this wrong I’m year 11 3u finished HSC 2u just for fun I’m doing 3u

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2. ## Re: Circle geo question

The theorem involving angles at the centre and circumference is only true when these angles are subtended by the same arc.

In this case, the angle $\angle C$ at the circumference is subtended by the arc $DAB$.

And the angle subtended by the same arc $DAB$ at the centre is the reflex angle at $\angle DOB$, which is what you have found instead (obviously, $230 ^\circ$ could not be the non-reflex angle).

The non-reflex angle $\angle DOB$ you are looking for is then $130 ^\circ$, and so $x = 65^\circ$.

This is easily verified:

$DABC$ is a cyclic quadrilateral.

$\therefore x = 180^\circ - \angle DCB = 65^\circ$ (opposite angles of a cyclic quad. are supplementary).

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