How to Construct Inscribed Circle of a Triangle? Class 10 Maths.
How to Construct Inscribed Circle of a Triangle? Class 10 Maths.
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How to draw an inscribed circle of a triangle?
We are to learn this technique, step by step in this video, by solving a typical problem.
The problem is. Draw a triangle with three arms of lengths 7 centimeter, 6 centimeter, and 5.5 centimeter. Draw the inscribed circle in it.
Let start.
At first, draw the length of the arms, as described in the problem. By using Scale and pencil. A 7 centimeter arm. A 6 centimeter arm. And a 5.5 centimeter arm.
Now, move the scale at lower middle portion of the page. And draw a large line segment there. Take a pencil compass. Move it to the 7 centimeter line segment. Stretch it about the length. Now, put the tip of the compass at the end point of this large line segment. And cut a 7 centimeter segment from this large line segment. Let this segment be called a b.
Next, move the pencil compass to 6 centimeter line segment. And stretch it to copy the length. Then, draw a small circle arc from point a. Again do the same for line segment of 5.5 centimeter. And, draw an arc from point b. In this way, the third angular point of the triangle is determined. Let this point be c.
Take the scale and pencil, and draw the arm a c. And then b c.
In this way, the required triangle is constructed.
Now, inscribed circle is to be drawn. To do so, any two angles of the triangle needs to be bisected. Here, we shall bisect angle A and angle b.
Let us bisect angle A first. Note the steps in this bisection procedure.
Then, bisection of angle b is to be done.
Let this two bisectors cross each other at point g.
Now, a perpendicular on arm A B is to be drawn, from point g.
To do so, take the pencil compass. And draw a large circle arc. This circle arc should intersect the arm A B twice. If you get only one point of intersection, or no intersection, the process will not work. So, adjust the pencil compass. And make sure, that it get two points of intersection.
Then, draw another two circle arcs from these two points of intersection. These two arcs meet each other at point h. Join these two points, g and h. G h is the perpendicular line on A B arm, from point g.
G h crosses the arm A B, at point m.
G m is the radius of the inscribed circle.
Finally, place the pencil compass on point g. And stretch it to length about g m. And draw the inscribed circle.
Sharper pencil and steady Geometric equipments can bring you the perfection.
Hope you realized the process. And are able to draw it yourself.
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