Question

1. in the figure FL=5 and HL= 8 what is FM (hint Pythagorean theorem and radi of circles)

Answer 1

1- FM is 3

we know that FM and FG are radius of the circle. so:
FM =FG


so if we find FG by Pythagorean theorem, we find FM, too


FL (hypotenuse) is 5

HL is 8. GL is half of HL. so GL is 4

now we can use Pythagorean theorem to find FG
$4 {}^{2} + {x}^{2} = {5}^{2} \\ {x}^{2} = {5}^{2} - {4}^{2} \\ {x}^{2} = 25 - 16 = 9 \\ x = \sqrt{9} = 3$




2- x is 40


BAD is half of m DB

ADB is half of m AB


so BAD is 50

and ADB is 90


Then ABD will be:
$180 - (50 + 90) = 180 - 140 \\ = 40$



good luck