Draw $\triangle ABC$ with $AB = 5$ cm, $\angle A = 100^\circ$, $AC = 4$ cm.
Draw the circumcircle of $\triangle ABC$. Is the centre inside or outside the triangle?                             [Page No. 98]

Construction steps:

1. Draw AB = 5 cm.

2. At A, construct ∠A = 100°, and mark C on this ray with AC = 4 cm.

3. Join BC to complete ΔABC.

4. Draw the perpendicular bisectors of AB and AC; they intersect at point O.

5. With O as centre and OA as radius, draw the circumcircle.

Since ∠A = 100° > 90°, ΔABC is an obtuse-angled triangle. Therefore, the circumcentre O lies outside the triangle.

Concept Applied
The circumcentre of a triangle lies inside an acute-angled triangle, on the hypotenuse of a right-angled triangle, and outside an obtuse-angled triangle.