Respuesta :

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

[tex] AB+CD = BC+AD [/tex]

In your case, we have

[tex]5+10=BC+8\iff 15=BC+8\iff 15-8=BC\iff BC=7[/tex]

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Answer:

[tex]7=BC[/tex]

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

[tex]AB+CD=BC+AD[/tex]

Substituting the given values, we have

[tex]5+10=8+BC[/tex]

[tex]15=8+BC[/tex]

[tex]15-8=BC[/tex]

[tex]7=BC[/tex]

Therefore the value of BC is 7.

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