Question

Given: Circumscribed quadrilateral ABCD, AB=5,
AD=8, CD=10.
Find: BC

Answer 1

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

`AB+CD = BC+AD`

In your case, we have

`5+10=BC+8\iff 15=BC+8\iff 15-8=BC\iff BC=7`

Answer 2

`7=BC`

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

`AB+CD=BC+AD`

Substituting the given values, we have

`5+10=8+BC`

`15=8+BC`

`15-8=BC`

`7=BC`

Therefore the value of BC is 7.