Question

Draw a circumcircle of a triangle whose sides are 10.5 cm, 12.7 cm and 13 cm respectively. Give reason, why the circumcentre of this triangle is inside the ΔABC.

Answer 1

Given :

Sides of triangle arc ABC, AB = 10.5 cm, AC = 12.7 cm and BC = 13 cm.

To construct:

Circumcircle of ΔABC.

(1) Taking A as center and radius 13 cm draw an arc. Taking B as center and radius 12.7 cm draw another arc which intersect the first arc at C.

(2) Join AC and BC. In this way we get ΔABC.

(3) Draw the perpendicular bisectors of AB and BC which intersect each other point O. Join O and A.

(4) Taking O as center and radius equal to OA draw a circle which passes through all the three vertices of ΔABC.

Since, constructed ΔABC is an acute angled triangle so its center lies inside the circle.