Name: Construction of Triangle When Base Angles and Perimeter Is Given
Uploaded: 2019-07-19
Duration: 5 min 46 s
Description: A perimeter and the three angles are a must for a triangle to exist. But you don't necessarily need all of these to construct a triangle. Let’s learn how in...

Question

Draw a triangle two of whose sides are

9 cm

and

7 cm

and the included angle between the sides is

60 °

. Construct the incircle of this triangle.

Accepted Answer

Steps of Construction:

(a) Draw a straight line $B C$ of length $9 cm$ . At $B$ draw an arc of any length such that it intersects $B C$ at $X .$

(b) With $X$ as centre and $B X$ as radius, draw an arc such that it intersects the arc drawn in step (a) at $Y$ .

(c) Join $B Y$ and extend the line up to the point $D$ . Thus, we get, $∠ D B C = 60 °$ .

(d) With $B$ as centre and taking $7 cm$ as radius, draw an arc on $A D$ , such that it intersects $A D$ at $A$ .

(e) Join $A C$ . Hence, we obtain the required triangle $△ A B C$ , whose sides are $9 cm$ and $7 cm$ and the included angle between the sides is $60 °$ .

(f) Draw the internal bisectors of $∠ B$ and $∠ C$ . Let these bisectors meet at $O$ . From $O$ draw perpendicular $O P$ to the side $B C$ .

(g) With $O$ as centre and radius equal to $O P$ draw a circle. This circle so drawn touches the sides $B C, C A$ and $A B$ at $P, Q$ and $R$ . Then the circle with $O$ as centre and $O P$ as radius is the required incircle of $Δ A B C$ .

Draw a triangle two of whose sides are $9 cm$ and $7 cm$ and the included angle between the sides is $60 °$ . Construct the incircle of this triangle.

Important Questions on Construction

Learn and Prepare for any exam you want !

Draw a triangle two of whose sides are 9 cm and 7 cm and the included angle between the sides is 60°. Construct the incircle of this triangle.

Important Questions on Construction

Learn and Prepare for any exam you want !

Draw a triangle two of whose sides are $9 cm$ and $7 cm$ and the included angle between the sides is $60 °$ . Construct the incircle of this triangle.