Question

Draw a triangle with two sides equal to 4 cm and 5 cm and the angle between them is 90${}^{\circ }$. Then the circumcentre of this triangle lies on the third side.

Answer 1

Draw triangle ABC with the given specifications, AB=4 cm, AC = 5 cm and $\angle$BAC = 90${}^{\circ }$.

Draw perpendicular bisectors of sides AB and AC, they meet at O. Join OB.

So, O is the centre and OB is the radius of the circumcircle of $△$ABC.

From the above constructions we see that the circumcentre O lies on the third side BC of $△$ABC.

Hence the given statement is true.