Prove that if chords of congruent circles subtend equal angles at their centres, thenthe chords are equal.
Text Solution
AI Generated Solution
To prove that if chords of congruent circles subtend equal angles at their centers, then the chords are equal, we can follow these steps:
### Step 1: Understand the Given Information
We have two congruent circles, and we know that the angles subtended by the chords at the centers of these circles are equal. Let’s denote the circles as Circle O1 and Circle O2, with chords AB and CD respectively. We are given that:
\[
\angle AOB = \angle COD
\]
...
Topper's Solved these Questions
CIRCLES
NCERT ENGLISH|Exercise Exercise 10.3|3 Videos
CIRCLES
NCERT ENGLISH|Exercise Solved Examples|6 Videos
AREAS OF PARALLELOGRAMS AND TRIANGLES
NCERT ENGLISH|Exercise Solved Examples|4 Videos
CONSTRUCTIONS
NCERT ENGLISH|Exercise EXERCISE 11.2|5 Videos
Similar Questions
Explore conceptually related problems
Prove that equal chords of congruent circles subtend equal angles at their centre.
Prove that equal chords of congruent circles subtend equal angles at their centre.
Prove Equal chords of congruent circles subtend equal angles at the centre.
Prove Equal chords of a circle subtend equal angles at the centre.
Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection
If the angles subtended by two chords of congruent circles at the corresponding centres are equal, then Prove chords are equal.
Prove Chords of congruent circles which are equidistant from the corresponding centres, are equal.
Prove that the line joining centres of two interesting circles subtends equal angles at the two points of intersection.
Equal chords of congruent circles are equidistant from the corresponding centres.
If two arcs of a circle (or of congruent circles) are congruent, then corresponding chords are equal.
