Class 9 Mathematics · Ganita Manjari Part 1

Class 9 Maths Chapter 5 – Exercise Set 5.2 Solutions

Question 1 — Show that the centre and a chord form an isosceles triangle

Let $AB$ be a chord of a circle with centre $O$. Join $OA$ and $OB$.

Since $OA$ and $OB$ are radii of the same circle,

Thus two sides of $\triangle OAB$ are equal.

Answer: $\triangle OAB$ is isosceles.

Question 2 — Equal bases give congruent triangles

Let $AB$ and $CD$ be equal chords of the same circle with centre $O$. Consider $\triangle OAB$ and $\triangle OCD$.

We have $OA=OC$ and $OB=OD$ because all are radii, and $AB=CD$ is given.

Therefore, by the SSS congruence criterion,

Answer: The two isosceles triangles are congruent by SSS.