Question

in a given figure O is the centre of a circle and xy is a diameter and xz is a chord prove that xy is greater than XZ

Answer 1

Given: A circle with centre o.

            xy is diameter and xz is chord.

To find: prove that xy > xz.

Solution:

step 1:

              join y and o points.

step 2:

              As we know that sum of any two sides in a triangle is always                 greater than 3rd side.

so,

In Δ xoz,

                     xo + oz > xz

                     xo + oy > xz          (oz = oy, as both are radius of circle.)

                     xy > xz                   ( xo + oy = xy, as it is clear from figure.)

Answer: so we have proved that  xy > xz

Answer 2

Step-by-step explanation:

Given;

O is the centre of the circle

XY is the diameter

XZ is the chord

To Prove;

XY > XZ

Proof;

step 1:

join OZ

step 2:

∆ OZX

=> OX + OZ > XZ

=> XY > XZ

Hence proved that XY > XZ.