Name: Types of Angles
Uploaded: 2019-07-19
Duration: 9 min 54 s
Description: A major portion of questions based on Geometry are based on angles and their determination. Let's understand what are angles and the types of angles....

Question

Draw an equilateral triangle of side

6.5 cm

and locate its incentre. Also draw the incircle.

Accepted Answer

The incentre is the point of intersection of the triangle’s three angle bisectors.

Steps of Construction:

Step $1 :$ Draw a line segment, $A B = 6.5 cm$ .

Step $2 :$ Taking a radius of $6.5 cm$ on compass draw an arc from point $A$ .

Step $3 :$ Similarly, draw an arc of same radius from point $B$ and let it meets the previous arc at $C$ .

Join $A, B, C$ . Thus, $△ A B C$ is formed.

Step $4 :$ With $A$ as centre and any radius draw arcs cutting $A C$ and $A B$ at $P$ and $Q$ . With $P$ as arc draw an arc and with $Q$ as centre draw at arc cutting the previous arc at $M$ . Join $A M$ .

Step $5 :$ With $B$ as centre and any radius draw arcs cutting $B C$ and $A B$ at $E$ and $F$ . With $E$ as arc draw an arc and with $F$ as centre draw at arc cutting the previous arc at $N$ . Join $B N$ .

The angle bisectors of the angles $∠ A$ and $∠ B$ meet at $I$ . $I$ is the incentre of $△ A B C$ .

Step $5 :$ Draw perpendicular from $I$ to the side $A B$ to meet $A B$ at $D$ .

Step $6 :$ With $I$ as centre, $I D$ as radius draw the circle. This circle touches all the sides of triangle internally.

Therefore, $I$ is the incentre and the circle with radius $I D$ is the incircle.

Draw an equilateral triangle of side $6.5 cm$ and locate its incentre. Also draw the incircle.

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