In right triangle $ABC$, $AC=BC$, arc $DEF$'s center is $A$, if the two shaded segments have the same area, what is $AD:DB$?

Asked Oct 06 '19 at 15:26

Active Oct 06 '19 at 16:17

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I'm working on this question for a math class I'm taking. I don't think it's very hard, but for some reason I can't really get anywhere with it. Since triangle $ABC$ is 45-45-90, I called $AD$ $x$ and $BD$ $y$, then drew line segment $AE$ and tried to find the areas of the shaded regions and set them equal to each other, but I had too many variables.

asked Oct 06 '19 at 15:26

Silverleaf1

1

If the shaded areas are equal then the area of the segment of the circle ADF equals the area of the right-angled triangle ABC. – Adam Rubinson Oct 06 '19 at 15:38
Thank you so much! – Silverleaf1 Oct 06 '19 at 15:44
No problem. What did you get for the answer? – Adam Rubinson Oct 06 '19 at 15:44
$1:\sqrt{\frac{\pi}{2}}-1$ – Silverleaf1 Oct 06 '19 at 15:56
Yeah that's what I got – Adam Rubinson Oct 06 '19 at 17:37

In right triangle $ABC$, $AC=BC$, arc $DEF$'s center is $A$, if the two shaded segments have the same area, what is $AD:DB$?

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