Name: Ruler and Compass Constructions
Uploaded: 2019-07-19
Duration: 9 min 30 s

Question

Construct an incircle on a right angle triangle. Find the value of the radius of the constructed circle.

Accepted Answer

Incircle of a triangle is inscribed in a triangle and touches each side of the triangle.

Let's take an example to understand the concept.

Example:
Construct an incircle of a right angle $△ A B C$ with sides $8 cm, 6 cm and 10 cm$ .

Solution :-

First we draw a line segment $B C = 8 cm$ .

We will draw a perpendicular using protractor on $B$

Open compass $6 cm$ and draw an arc from point $B$ on the perpendicular.

Again draw an arc of $10 cm$ taking centre as $C$ .

These both arcs intersect each other at a point and name that point as $A$ .

Join $A C and A B$ .

Then, triangle $A B C$ is the required right angled triangle.

After that we bisect $∠ A and ∠ C$ .

The bisectors of these two angle cut at point $O$ .

Then, draw a perpendicular on $B C$ from the point $O$ and it cuts the $B C$ at $D$ .

Then, draw a circle with the radius $O D$ and it will touches each side of the triangle with centre as $O$ .

The resultant circle is the required circle with centre $O$ .

To find the radius of a circle inside a right angled triangle, we have the formula to find the radius of the right angled triangle, $r = \frac{(P + B - H)}{2}$ . Given the $P, B and H$ are the perpendicular, base and hypotenuse respectively of a right angled triangle.

$r = \frac{(6 + 8 - 10)}{2} = \frac{4}{2} = 2 cm$

Construct an incircle on a right angle triangle. Find the value of the radius of the constructed circle.

Important Questions on Geometrical Constructions

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