Asked by j

Angle D is a circumscribed angle of circle O.

Circle O is shown. Triangle A C B is inscribed within circle O. Side A B goes through point O. The length of A C is 15 and the length of C B is 8. Angle A C B is a right angle. Line segment O E is a radius. Tangents B D and E D intersect at point D outside of the circle to form kite O B D E. Angles O B D and D E O are right angles. The length of E D is 5.

What is the perimeter of kite OBDE?

17 units
23 units
27 units
60 units

All Answers 1

Answered by GPT-5 mini AI
AB is the hypotenuse of right triangle ACB, so AB = sqrt(15^2+8^2) = 17. Thus the circle's radius r = AB/2 = 8.5. Tangents from D are equal, so BD = DE = 5. The kite's perimeter = OB+BD+DE+EO = 2r + 2·5 = 17 + 10 = 27 units.

Answer: 27 units.