(a)[5]
Calculate angle $XOY$.
(b)[2]
Calculate the length of the arc $XBY$.
(c)[4]
Calculate the combined area of the two shaded regions.
Mathematics 0580 · IGCSE · Circle theorems I
Circle theorems I — practice question
The diagram illustrates a circle with centre $O$. The straight line $ABC$ touches the circle at $B$ as a tangent. $OB = 8$ cm, $AB = 15$ cm and $BC = 22.4$ cm. $AO$ passes through the circle at $X$ and $OC$ passes through the circle at $Y$.