Points $a$, $b$, and $c$ are on a circle such that $ab = 8$, $bc = 15$, and $ac = 17$. find the radius of the circle.

radius is 8.5

Step-by-step explanation:

Points A, B, and C are on a circle such that AB = 8, BC = 15, and AC = 17. Looking at the three points, they form a Pythagorean triple. This is so because

17^2 = 8^2 + 15^2

289 = 64 + 225 = 289

This means that the triangle formed by the three points is a right angle triangle. A right angle triangle inscribed in a circle subtends an angle of 90 on the circumference of the circle. This means that the longest side or hypotenuse of the triangle becomes the diameter of the circle. Therefore,

Diameter = 17

Radius = diameter /2 = 17/2 = 8.5

step-by-step explanation:

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