West Bengal Board Solutions for Chapter: Geometrical Proofs, Exercise 6: Let's Work Out - 20.3

Two persons one of them is coming along south direction to reach to east-west road and other person is coming along the south-east direction starting from the same place. Let's calculate which person reaches first to the road.

In a quadrilateral $ABCD, AB=AD \text{and} BC=DC$ and $DP$ is the smallest distance drawn from $D$ on $AC$. Let's prove that $B, P$ and $D$ are collinear.

$AD$ is a median of the triangle $ABC$. The smallest distance of $AD$ from $B \text{and} C$ are $BP \text{and} CQ$ respectively. Let's prove that $BP=CQ$.