IPMAT Indore (MCQ) PYQs

On a circular path of radius 6 m a boy starts from a point $A$ on the circumference and walks along a chord $AB$ of length 3 m. He then walks along another chord $BC$ of length 2 m to reach point $C$. The point $B$ lies on the minor arc $AC$. The distance between point $C$ from point $A$ is

If the shortest distance of a given point to a given circle is $4 \, \text{cm}$ and the longest distance is $9 \, \text{cm}$, then the radius of the circle is

A circle of radius $13$ cm touches the adjacent sides AB and BC of a square ABCD at M and N, respectively. If AB = $18$ cm and the circle intersects the other two sides CD and DA at P and Q, respectively, then the area, in sq. cm, of triangle PMD is