SOLUTION: 3 concentric circles have radii of 5 cm, 10 cm and 15 cm. the chords of the two larger circles are tangent to the two smaller circles, and the point of tangency both lie on the rad

Algebra ->  Circles -> SOLUTION: 3 concentric circles have radii of 5 cm, 10 cm and 15 cm. the chords of the two larger circles are tangent to the two smaller circles, and the point of tangency both lie on the rad      Log On


   

Question 1093391: 3 concentric circles have radii of 5 cm, 10 cm and 15 cm. the chords of the two larger circles are tangent to the two smaller circles, and the point of tangency both lie on the radius of the larger circle. find the area of the quadrilateral region determine by the radios of the chord.
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Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

Let the common center of the three circles be O.
Let OA be a radius of the large circle, intersecting the smallest circle and middle circle at B and C, respectively.
Let DE be the chord of the middle circle tangent to the small circle at B; let FG be the chord of the largest circle tangent to the middle circle at C.

Then the quadrilateral whose area we are to find is EDFG. By symmetry, we can see that this is an isosceles trapezoid with bases DE and FG and height BC. We know BC is 5cm; so we can find the area of the trapezoid if we know the lengths of the bases DE and FG.

But we can find those lengths using the Pythagorean Theorem on triangles OBD and OCF.

I leave it to you to finish the problem from there.