Multiple choice

Find the co-ordinate of the circumcentre of the triangle whose vertices are (8,6),(8,-2) and (2,-2) then the radius of the circumcircle.

  1. 10 units

  2. 5 units

  3. 2.5 units

  4. 25 units
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The triangle is right-angled at (8,-2), so its circumcentre is the midpoint of the hypotenuse joining (8,6) and (2,-2), namely (5,2). The hypotenuse has length 10 units, so the circumradius is 5 units, matching option B.

AI explanation

Let the vertices be A(8,6), B(8,-2) and C(2,-2), which form a right-angled triangle at B because AB is a vertical line and BC is a horizontal line. By the property of right-angled triangles, the hypotenuse AC is the diameter of the circumcircle. Using the distance formula, the radius is half of AC, calculated as 0.5 * sqrt((8-2)^2 + (6 - (-2))^2) = 0.5 * sqrt(36 + 64) = 0.5 * 10 = 5 units.

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