The circumcircle of a given ∆ABC is drawn. Can there be other triangles congruent to ∆ABC Class 9

The circumcircle of a given ∆ABC is drawn. Can there be other triangles congruent to ∆ABC Class 9

Question 1.

The circumcircle of a given ∆ABC is drawn. Can there be other triangles congruent to ∆ABC that share the same circumcircle? Class 9

Answer:

Yes, other triangles congruent to ∆ABC can share the same circumcircle. They can be obtained by rotating or reflecting ∆ABC on the same circle.

Question 2.

Show that the triangle formed by a chord and the centre of the circle is isosceles. Class 9

Answer:

Given: AB is any chord of a circle with centre O

To show: ∆OAB is an isosceles triangle

Proof:

Join OA and OB.

OA and OB are the radii of the same circle

∴ OA = OB = r

∴ ∆OAB is an isosceles triangle.