Question

In figure, O is the centre of the circle.
Line AB, BC, CD and DA touches
the circle in point E, F G and H
respectively. Show that in ABCD
T
Q
A
E
B В
o
F
of opposite sides are equal.
H
sum
D
G​

Answer 1

Given : Line AB, BC, CD and DA touches the circle in point E, F G and H

respectively

To Find : Show that sum of opposites sides of Quadrilateral ABCD is equal

Solution:

AB, BC, CD and DA touches the circle in point E, F G and H

AE = AH       Equal Tangents

BE = BF       Equal Tangents

CF = CG      Equal Tangents

DG = DH      Equal Tangents

AE  + BE  + CG + DG  = AH + BF + CF  + DH

=>  ( AE + BE) + (CG + DG) = (AH + DH) + (BF + CF)

=>  AB + CD = AD + BC

QED

Hence Proved

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