Problem #5: Triagley thing

[Silly Druid 6,144]

Let's do some geometry for a change:

Both circles here are the same size. Calculate their radius.

Edited November 21, 2023 by Silly Druid

[Brony Number 42 9,933]

r = 5 / 7

What do you think?

[SasQ 1,355]

Ah, geometry, my favorite :>

The answer seems to be correct, although using trigonometry for such a problem is kinda like picking a sledgehammer to crack a nut

Notice that the line connecting the centres of the circles (the double radius) is parallel to the hypotenuse, so if you project these points on the other two legs, you'll get a smaller triangle which has the same shape as the original one (i.e. they're similar, and hence their sides are in proportion). From that you should be able to construct an equation for `r` in terms of the sides.

[Brony Number 42 9,933]

5 hours ago, SasQ said:

Notice that the line connecting the centres of the circles (the double radius) is parallel to the hypotenuse

That was the key to my solution.