Let equal chords AB and CD intersect at P. Since the chords are equal, their corresponding parts have equal sums. Using the intersecting-chords theorem and equality of the chords, we get AP = CP and BP = DP. Hence proved.
When two chords intersect, each of them is divided into two line segments. Show that if the intersecting chords are of equal length, then the line segments of one chord are equal to the corresponding line segments of the other chord.
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Let equal chords AB and CD intersect at P. Since the chords are equal, their corresponding parts have equal sums. Using the intersecting-chords theorem and equality of the chords, we get AP = CP and BP = DP. Hence proved.
75 Words Answer:
Let equal chords AB and CD intersect at P. Since AB = CD, we have
AP + PB = CP + PD.
Also, by the intersecting chords theorem,
AP × PB = CP × PD.
Thus, the two pairs of segments have equal sum and equal product. Therefore, the corresponding segments are equal.
Hence,
AP = CP and PB = PD.
Therefore, if two equal chords intersect, their corresponding line segments are equal. Hence proved.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 5 I’m Up and Down and Round and Round (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-5/