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