Circle and a quadrilateral

$\begingroup$

Q: The polygon circumscribes the circle. Find the perimeter.

$\endgroup$ 3

2 Answers

$\begingroup$

It is a fact that any two intersecting tangents are equal in length.

Thus, the perimeter is $2(9+7+5+8)=58$

$\endgroup$ $\begingroup$

It's a basic theorem in euclidean geometry: a quadrilateral circumscribes a circle iff the sum of the lengths of both pairs of opposite sides is the same. This follows at once from the fact that Amr reminds in his answers: both tangents to a circle from an exterior point to the circle have the same length.

From this the perimeter of your quadrilateral is 58.

$\endgroup$

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy