Answer:
46 inches
Explanation:
You want the perimeter of ABCD, where AB and BC are tangent to circle D, and AB = 15 inches, BD = 17 inches.
Figure
The attachment shows the figure. Radii DA and DC are perpendicular to the tangens, so each triangle is a right triangle. The hypotenuse BD is given as 17 inches, and the leg AB is given as 15 inches. The other leg is found from the Pythagorean theorem (or from your knowledge of Pythagorean triples). It is ...
AD = √(DB² -AB²)
AD = √(17² -15²) = √(289 -225) = √64
AD = 8
Perimeter
The perimeter is the sum of side lengths. The kite shape is symmetrical, so the perimeter is ...
P = 2(AD +AB) = 2(8 +15) = 46 . . . . inches
The perimeter of ABCD is 46 inches.
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