Given: circumscribed quadrilateral abcd, ab=5,
ad=8, cd=10.
find: bc

In a circumscribed quadrilateral, the sum of the lengths of opposite sides is constant:

In your case, we have

Step-by-step explanation:

It is given that a quadrilateral ABCD is inscribed in circle and AB=5, AD=8 and CD=10.

Then, using the properties of the quadrilateral inscribed in circle that is the sum of the lengths of opposite sides of quadrilateral  are equal, we have

Substituting the given values, we have

Therefore the value of BC is 7.

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