Area Problem #7

circley problem

If the area of the right angled triangle is 60cm2, find the area of the circle.

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10 thoughts on “Area Problem #7

  1. Hi

    I have solved this to get r=20 by finding the equation of the radius crossing the hypotenuse at right angles in terms of r. Then finding where they intersect again in terms of r and finally using pythagoras to get a quadratic in terms of r. Is there a simpler method?

    • I found all 3 sides of the triangle first, then drew a square from the centre of the circle to the top tangent and right angled point of the triangle. You can then get two simple equations using a combination of r a b and c, then solve for r. Your answer is correct.

  2. A solution that is mostly definitions. Label the points of intersection (chosen to suit the conclusion, above, that r=(a+b+c)/2 using the sides of the triangle):
    * D, A, C: on the top horizontal line,
    * C, B, E: on the right vertical line,
    * F: the center, and
    * G: the triangle’s tangent point with the circle
    Define:
    * a = BC (15 in the example)
    * b = AC (8 in the example)
    * c = BC (17 in the example)
    * r = radius
    By “tangents to a circle are congruent”, both:
    * BG = BE = r-a
    * AG = AD = r-b
    Also:
    * AG+BG = AB = c
    So:
    * (r-a)+(r-b)=c
    Or 2r=a+b+c

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