Question

(a) Draw triangle $ABC$ with $AB=10cm,\angle A={50}^{\circ }$ and $\angle B={70}^{\circ }$.
(b) Draw the incircle of triangle $ABC$ and write the measure of its radius.

Answer 1

Given: $AB=10cm,m\angle A={50}^{\circ }$ and $m\angle B={70}^{\circ }$
Steps of Construction:
$1$. Draw $AB=10cm$
$2.$ At $A$, construct $m\angle PAB={50}^{\circ }$
$3.$ At $C$, construct $m\angle OBA={70}^{\circ }$ to meet the line $AP$ at $C$.
Thus, $△ABC$ is the required triangle.
(b) Steps for incircle of a triangle.
$1.$ Bisect $\angle BAC$ and $\angle ABC$. Let the bisectors meet at point $O$.
$2.$ From point $O$, draw perpendicular to the side $AB$ to meet $AB$ at the point $P$.
$3.$ Draw a circle with centre $O$ and radius $OP$.
Radius $OP=3cm$.