Question : A quadrilateral $ABCD$ circumscribes a circle and $AB=6\operatorname{cm},CD=5\operatorname{cm},$ and $AD=7\operatorname{cm}$. The length of side $BC$ is:
Option 1: 4 cm
Option 2: 5 cm
Option 3: 6 cm
Option 4: 3 cm
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Correct Answer: 4 cm
Solution :
In a quadrilateral that circumscribes a circle, the sum of a pair of opposite sides is equal to the sum of the other pair of opposite sides.
We know that the tangents from a point to a circle are equal in length.
In quadrilateral $ABCD$,
$AB + CD = AD + BC$
$⇒6+5= 7+ BC$
$\therefore BC =4\operatorname{cm}$
Hence, the correct answer is 4 cm.
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