In a circle, two chords CC' and DD' are drawn perpendicular to a diameter AB. Prove that the segment Class 9

In a circle, two chords CC' and DD' are drawn perpendicular to a diameter AB. Prove that the segment Class 9

Question 1.

In a circle, two chords CC' and DD' are drawn perpendicular to a diameter AB. Prove that the segment MM' joining the midpoints of the chords CD and C'D' is perpendicular to AB. Class 9

Solution:

Given: AB is diameter

CC' ⊥ AB, DD' ⊥ AB

To Show: MM' ⊥ AB

Since CC' ⊥ AB and AB passes through centre O

∴ AB bisects CC'

∴ C and C' are symmetric about AB

Similarly,

D and D' are symmetric about AB

∴ Segment CD and C'D' are mirror images about AB

Given M is midpoint of CD and M' is midpoint of C' D'

Since midpoints of mirror segments are also mirror images

∴ Line joining a point and its mirror image is perpendicular to the mirror line

∴ MM' ⊥ AB