Question

Using ruler and compasses only, construct an isosceles$\Delta ABC$
in which $BC=5$ cm, $AB=AC$ and$\angle BAC$ $=$ ${90}^0$ Locate the point $P$ such that:
(i) $P$ is equidistant from $BC$ and $AC$.
(ii) $P$ is equidistant from $B$ and $C$.

Answer 1

Steps of constructions are:

(1) Draw a line segment AC of any length and draw a ray AX making an angle of ${90}^0$ with AC. Cut off AB and join BC.

(2) Draw the perpendicular bisector of AC.

(3) Points equidistant from B and C lies on the perpendicular bisector of BC. Draw perpendicular bisector of BC. The required point P is the point of intersection of the bisector of $\angle ABC$ and the perpendicular bisector of BC.