Question

Draw triangle ΔABC with measurements as given below and draw the circum-circle of each:

(a) AB = 4 cm, AC = 5 cm, ∠A = 60°

(b) AB = 4 cm, AC = 5 cm, ∠A = 120°

(c) AB = 4 cm, AC = 5 cm, ∠A = 90°

Note the position of the circum-centre of each triangle. Draw more triangles and see whether any general conclusion can be formed.

Answer 1

(a)

The dimensions of the required triangle are AB = 4 cm, ∠A = 60° and CA = 5 cm.

The steps of construction are as follows:

1) Draw a line segment AB of length 4 cm.

2) Draw ∠TAB of measure 60° at point A.

3) Mark an arc on AT by taking A as the centre and 5 cm as the radius. Name the point of intersection as C.

4) Join CB.

ΔABC is the required triangle.

Circumcircle of the triangle can be constructed as follows:

1) Draw perpendicular bisectors of AB and BC such that they intersect at point O.

2) With O as the centre and radius OA (or OB or OC), draw a circle passing through the points A, B and C.

The given figure shows the circumcircle of ΔABC.

(b)

The dimensions of the required triangle are AB = 4 cm, ∠A = 120° and CA = 5 cm.

The steps of construction are as follows:

1) Draw a line segment AB of length 4 cm.

2) Draw ∠TAB of measure 120° at point A.

3) Mark an arc on AT by taking A as the centre and 5 cm as the radius. Name the point of intersection as C.

4) Join CB.

ΔABC is the required triangle.

Circumcircle of the triangle can be constructed as follows:

1) Draw perpendicular bisectors of AB and BC such that they intersect at point O.

2) With O as the centre and radius OA (or OB or OC), draw a circle passing through the points A, B and C.

The given figure shows the circumcircle of ΔABC.

(c)

The dimensions of the required triangle are AB = 4 cm, ∠A = 90° and CA = 5 cm.

The steps of construction are as follows:

1) Draw a line segment AB of length 4 cm.

2) Draw ∠TAB of measure 90° at point A.

3) Mark an arc on AT by taking A as the centre and 5 cm as the radius. Name the point of intersection as C.

4) Join BC.

ΔABC is the required triangle.

Circumcircle of the triangle can be constructed as follows:

1) Draw perpendicular bisectors of AB and BC such that they intersect at point O.

2) With O as the centre and radius OA (or OB or OC), draw a circle passing through the points A, B and C.

The given figure shows the circumcircle of ΔABC.