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Forum ยป High IQ math question
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Thread: High IQ math question

post 1627880163 01-08-2021, 03:14 AM
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High IQ math question

https://ibb.co/SJKGS8S

In the diagram, KLJ is right angled at J, with JK=3 and JL=4.
KLJ is inscribed in a quarter circle with radius ML, as shown.

What is the area of the quarter circle?
post 1627880543 01-08-2021, 03:31 AM
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about 350/22.2816920329
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post 1627880783 01-08-2021, 03:38 AM
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(lm^2*pie)/4
post 1627880973 01-08-2021, 03:50 AM
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5pi if K is the midpoint. I do not think it shows enough information if not.

proof:

3,4 sides of a right triangle --> AL = 5.

a, 2a, 5 right triangle --> 5a^2 = 25. a^2 = 5.

2a = 2sqrt(5).

Circle = pi*4*5 = 20 pi.
1/4 circle = 5 pi.

Other right angles can exist from simply adjusting J and K in the same vertical direction along their curves, so without K as a midpoint, so I do not think you can say much from dimensions of an inscribed right triangle alone without more information.
post 1627881443 01-08-2021, 04:11 AM
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5.0000090449(pi)

or

[4.47214^2 (pi)]/4
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post 1627881713 01-08-2021, 04:21 AM
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