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Question

In fig., a circle touches all the four sides of a quadrilateral $$ABCD$$ in which $$AB = 6 cm, BC = 7 cm$$ and $$CD = 4 cm$$. Find $$AD$$.

Solution
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Given,
$$AB=6cm,BC=7cm,CD=4cm$$
We know that
$$\boxed{\text{When a circle inscribed in a quadrilateral ABCD touching all the four sides then AB+CD = BC+AD}}$$
$$\Rightarrow 6+4=7+AD$$
$$\Rightarrow 10=7+AD$$
$$\Rightarrow AD=10-7$$
$$\Rightarrow AD=3$$

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