Q1. Show that the triangle formed by a chord and the centre of the circle is isosceles.

Answer:

Let AB be a chord of a circle with centre O. Consider triangle OAB.

OA and OB are both radii of the circle, so OA = OB.

Since two sides of triangle OAB are equal, it is an isosceles triangle.

Q2. Show that if two such isosceles triangles (occurring in the previous question) have equal base length, they are congruent to each other.

Answer:

Let the two triangles be OAB and OCD, where O is the centre of the circle and AB and CD are two chords of equal length.

We know:

• OA = OB = OC = OD (all are radii of the circle)
• AB = CD (given: equal base length)

By the SSS (Side-Side-Side) congruence criterion, triangle OAB is congruent to triangle OCD.