Question

Draw a triangle ABC with AB = 3 cm, BC = 4 cm and ∠B = 60°. Also, draw the bisector of angles C and A of the triangle, meeting in a point O. Measure ∠COA.

Answer 1

Steps of construction:

1. Draw a line segment BC = 4 cm.
2. Draw $\angle CBX\hspace{0.17em}=60°$.
3. Draw an arc on BX at a radius of 3 cm cutting BX at A.
4. Join AC to get the required triangle.

Angle bisector for angle A:

1. With A as centre, cut arcs of the same radius cutting AB and AC at P an Q, respectively.

2. From P and Q cut arcs of same radius intersecting at R.

3. Join AR to get the angle bisector of angle A.

Angle bisector for angle C:

1. With A as centre, cut arcs of the same radius cutting CB and CA at M an N, respectively.

2. From M and N, cut arcs of the same radius intersecting at T.

3. Join CT to get the angle bisector of angle C.

Mark the point of intersection of CT and AR as O.

Angle $\angle$COA = 120^o