Home
Class 9
MATHS
If two equal chords of a circle interse...

If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.

Text Solution

AI Generated Solution

To prove that the line joining the point of intersection of two equal chords to the center of the circle makes equal angles with the chords, we can follow these steps: ### Step-by-Step Solution: 1. **Given Information**: We have two equal chords AB and CD of a circle that intersect at point X inside the circle. We need to prove that the angles formed by the line joining the center O of the circle to the point X with the chords are equal, i.e., ∠OXA = ∠OXD. 2. **Construct Perpendiculars**: ...
Promotional Banner

Similar Questions

Explore conceptually related problems

prove that the line joining the mid-point of two equal chords of a circle subtends equal angles with the chord.

If two equal chords of a circle in intersect within the circle, prove that : the segments of the chord are equal to the corresponding segments of the other chord. the line joining the point of intersection to the centre makes equal angles with the chords.

If two equal chords of a circle in intersect within the circle, prove that: the segments of the chord are equal to the corresponding segments of the other chord. the line joining the point of intersection to the centre makes equal angles with the chords.

Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord.

If two equal chords of a circle in intersect within the circle, prove that: the segments of the chord are equal to the corresponding segments of the other chord.

If two equal chords of a circle intersect within the circle, prove that: the segments of the chord are equal to the corresponding segments of the other chord.

If the two equal chords of a circle intersect : (i) inside (ii) on (iii) outside the circle, then show that the line segment joining the point of intersection to the centre of the circle will bisect the angle between the chords.

If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.

If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.

Prove that the line joining centres of two interesting circles subtends equal angles at the two points of intersection.