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

Question

Construct incircle and circumcircle for triangle

A B C

, when

A B = 3 c m, B C = 4 c m & ∠ B = 90 °

. Also find the radius of the incircle and circumcircle.

Accepted Answer

Steps of construction circumcircle:

Draw a triangle $A B C$ .

Draw a perpendicular bisector on side $A B$ and $B C$ which intersects $A B$ at $P$ and $B C$ at $Q$ . the perpendicular bisectors intersect each other at $O$ .

Now draw a circle by taking $O$ as a reference and with $O A$ as a radius. We can see that this circle is passing through all three vertices.

Steps of construction in circle:

Draw a triangle $A B C$ .

Draw angle bisectors of angle $A B C$ and angle $B C A$ . The point at which both cut each other is taken as the center $O$ .

Now draw a perpendicular from the point $O$ to side $B C$ which intersects $B C$ at $Q$ .

Draw a circle taking $O$ as a center and $O Q$ as a radius. We can see that this circle touches all the three sides.

Hence, the perpendicular distances $A B, A C & C A$ from $O$ are same.

Now with the help of ruler measure the radius of in circle and circumcircle.

The radius of incircle is $1 c m$ and the radius of circumcircle is $2.5 c m$ .

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