Question

A triangle has its sides as 10 cm, 11 cm, and 15 cm. Its circumcentre lies:

Answer 1

outside, as the triangle is obtuse

Answer 2

Answer:  The circumcentre will lie outside the triangle.

Step-by-step explanation:  Give that a triangle has three sides of length 10 cm, 11 cm and 15 cm.

As shown in the attached figure, ΔABC is drawn, where AB = 10 cm, BC = 11 cm and CA = 15 cm.

AB² = 100, BC² = 121 and CA² = 225.

Therefore, CA² > AB² + BC². That is, ΔABC is an obtuse-angled triangle.

To draw the circumcentre, we foirst draw the perpendicular bisectors of AB, BC and CA. We see that these perpendicular bisectors meets at a point P, which lies outside the triangle.

Thus, the circumcentre of an obtuse-angled triangle will lie outside the triangle.