5. 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 sum of opposite sides are equal.
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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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