Construct the triangle ABC with AB = 5cm, BC = 6cm. and CA = 7cm and draw the circumcircle.
Steps for construction:
- Draw a line segment AB = 5cm.
- With A as center and radius 7cm, draw an arc.
- With B as center and radius 6cm, draw another arc that cuts first arc at the point C.
- Join BC and CA (AC = CA).
- Draw the perpendicular bisectors of AB, BC and CA.
- Let them intersect at S.
- With S as centre and SA (=SB = SC) as radius draw a circle.
- This circle passes through the three vertices of the triangle A, B and C.
This is the circumcircle of the given triangle.
Directions: Read the above review points carefully and answer the following questions:
- Draw the circumcircle of the triangle ABC whose with sides are given by AB = 6 cm, BC = 7 cm and CA = 9 cm.
- Draw circumcircles of acute, right and obtuse angled triangles. Discuss the position of circumcentre's obtained.