IIMB 2000 (QA) PYQs

The centre of the circle which passes through points $A$,$B$ and $C$ is $'O'$. If $\angle BAO=30\degree$, $\angle BCO=40\degree$ and $\angle AOC=x\degree$. Then find the value of $x$.

From an external point $P$, tangents $PA$ and $PB$ are drawn to two concentric circles with center $O.$ The larger circle has a radius of $8$ cm, and the smaller circle has a radius of $5$ cm. If the length of $AP$ is $15$ cm, find the length of $BP.$

In a circle with a radius of $13$ cm, two parallel chords, $EF$ and $GH$, are on the same side of the circle. Chord $EF$ measures $10$ cm, and chord $GH$ measures $24$ cm. Determine the distance between these two chords.