Question

Using ruler and compasses only, construct a triangle ABC in which BC $=4$ cm, $\angle ACB={45}^{\circ }$ and the perpendicular from A on BC is $2.5$ cm. Draw the circumcircle of triangle ABC and measure its radius.

Answer 1

1)Draw a line segment $BC=4$ cm.

2)At $C$. Draw $C$ $\perp$ line $CX$ and from it cut off $CE=2.5$ cm.

3)From $E$, Draw another $\perp$ line $EY.$

4)From $C$, Draw a ray making on $\angle {45}^{\circ }$ with $CB,$ which intersects $EY$ at $A.$

5)Join $AB.$ Thus $△ABC$ is the required $△$le.

6)Draw bisector of sides $AB$ and $BC$ intersecting each other at $O.$

7)With centre $O,$ and radius $OB$, Draw a circle which will pass through $A,B$ and $C.$ Measuring the radius $OB=OC=OA=2$ cm.