19. A circle is inscribed in a quadrilateral ABCD.
If AB = 5 cm, BC = 6 cm and CD = 8 cm, find
the length of side AD.
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Answer:
A circle with centre O, touches the sides AB,BC,CD,DA, at P,Q,R,Srespectively.
Join OP,OQ,OR,OS
Now two tangents drawn from an external C
point to a circle subtend equal angles at
the centre.
∴(i)AP=AS, (ii)BP=BQ,(iii)CR=CQ, (iv)DR=DS
AB=6 cm,BC=7 cm,CD=4 cm
Now from above solution we have
AB+CD=BC+AD
⇒10=7+AD
⇒AD=3 cm
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