Find the perimeter of the cyclic quadrilateral ABCD shown.

Question

Find the perimeter of the cyclic quadrilateral ABCD shown.

B

1. Each vertex of the quadrilateral is on the edge of the circle.
2. The first side of the quadrilateral starts at vertex A and goes vertically up to vertex B. It is labeled 51.
3. The second side of the quadrilateral starts at vertex B and goes horizontally to the right to vertex C. It is labeled 68.
4. The third side of the quadrilateral starts at vertex C and goes down and to the left to vertex D. It is not labeled.
5. The fourth side of the quadrilateral starts at vertex D and goes up and to the left to vertex A. It is labeled 36.

Answer 1

Assume the cyclic quadrilateral ABCD is shown as below, by applying pythagorean theorem, calculate CD then get the perimeter P=AB+BC+CD+DA=148+CD≈219

BC=61

BA=51CD²=BC²+BA²-AD²≈71

AD=36