Question

(i) Construct a triangle $ABC$ with $BC=6.4cm,CA=5.8cm$ and $\angle ABC={60}^{\circ }$. Draw its incircle. Measure and record the radius of the incircle.
(ii) Construct a $△ABC$ with $BC=6.5cm,AB=5.5cm,AC=5cm$. Construct the incircle of the triangle. Measure and record the radius of the incircle.

Answer 1

(i) Steps to construct:
Step 1: Draw a line segment $BC=6.4cm$.
Step 2: Construct an angle of ${60}^{\circ }$ at point $B$.
Step 3: With $C$ as the center and radius $CA=5.8cm$, draw an arc Cutting $BD$ at $A$.
Step 4: Join $AC$.
Step 5: Draw the angle bisector of angle $B$ and $C$ which intersects each other at point $O$.
Step 6: Draw $OE$ perpendicular to $BC$, intersecting $BC$ at point $E$.
Step 7: With $O$ as the center and $OE$ as the radius draw the required incircle.
Step 8: On measuring the radius $OE=1.5cm$.
(ii) Steps to construct:
Step 1: Draw a line segment $BC=6.5cm$.
Step 2: With $B$ as center and $C$ as center draw arcs $AB=5.5cm$ and $AC=5cm$.
Step 3: Join $AB$ and $AC$.
Step 4:Draw the angle bisector of $B$ and $C$. The bisectors meet at point $O$.
Step 5: With $O$ as the center. Draw an incircle which touches all the sides of the triangle $ABC$.
Step 6: From point $O$ draw a perpendicular to side $BC$, which cuts at point $N$.
Step 7:On measuring the radius $ON=1.5cm$.