List of top Quantitative Ability and Data Interpretation Questions on Geometry asked in XAT

Consider a square $ABCD$ of side $60$ cm. It contains arcs $BD$ and $AC$ drawn with centres at $A$ and $D$ respectively. A circle is drawn such that it is tangent to side $AB$, and the arcs $BD$ and $AC$. What is the radius of the circle?

In a plane rectangular coordinate system, points $L, M, N,$ and $O$ are represented by the coordinates $(-5,0), (1,-1), (0,5),$ and $(-1,5)$ respectively. Consider a variable point $P$ in the same plane. The minimum value of $PL + PM + PN + PO$ is:

Let $PQRS$ be a quadrilateral. Two circles $O_1$ and $O_2$ are inscribed in triangles $PQR$ and $PSR$ respectively. Circle $O_1$ touches $PR$ at $M$ and circle $O_2$ touches $PR$ at $N$. Find the length of $MN$. % Statement I A circle is inscribed in the quadrilateral $PQRS$. % Statement II The radii of the circles $O_1$ and $O_2$ are 5 and 6 units respectively.

The points (–4, 3) and (–1, –4) are two end points of a diagonal of a parallelogram. If the other diagonal has the equation 7y + 3x + c = 0, then find the value of c.