In Fig. 10.12, ∠ABC = 45º, prove that OA ⊥ OC.

Solution:

Given, ∠ABC = 45º

We have to prove that OA ⊥ OC

We know that the angle subtended by an arc of a circle at the center is double the angle subtended at the remaining part of the circle by the same arc.

So, ∠AOC = 2 ∠ABC

∠AOC = 2(45º)

∠AOC = 90º

This implies OA is perpendicular to OC

Therefore, OA ⊥ OC

✦ Try This: In figure, O is the centre of the circle, then find the value of x.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 10

NCERT Exemplar Class 9 Maths Exercise 10.3 Sample Problem 2

In Fig. 10.12, ∠ABC = 45º, prove that OA ⊥ OC.

Summary:

A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) in the plane. In Fig. 10.12, ∠ABC = 45º, it is proven that OA ⊥ OC

☛ Related Questions:

• If arcs AXB and CYD of a circle are congruent, find the ratio of AB and CD
• If the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q, pro . . . .
• A, B and C are three points on a circle. Prove that the perpendicular bisectors of AB, BC and CA are . . . .