Find the value of x. FG perpendicular to OP, RS perpendicular to OQ, FG=20, RS=24, OP=14

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Find the value of x. FG perpendicular to OP, RS perpendicular to OQ, FG=20, RS=24, OP=14

Mathematics
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let r = radius of the circle

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Other answers:

by the pythagorean theorem, we can say (FP)^2 + (OP)^2 = (OF)^2 10^2 + 14^2 = r^2 solve for r and tell me what you get
100 + 196 = 296^2. Now what?
r^2 = 296 so r = ???
296
no
r^2 is 296, not r
87, 616
don't square it though
how do you undo squaring something
sqrt?
yep
16.9?
you did sqrt(296) right?
Yea
it's close, but not correct
sqrt(296) = 17.2046505340852 round to whatever place you need to
17.2 isn't one of the answers. Only 16.9
but remember, we want x, not r
we use r to get x
the possible answers are: 16.9, 14, 12.3, and 12..
\[\large r = \sqrt{296} \rightarrow r^2 = 296\] \[\large (OQ)^2 + (RQ)^2 = (OR)^2\] \[\large (OQ)^2 + (RQ)^2 = r^2\] \[\large x^2 + 12^2 = 296\] \[\large x^2 + 144 = 296\] ... ... ... \[\large x = ???\]
152
12.3
\[\large x^2 = 152\] so \[\large x = ???\]
good, x is roughly 12.3
What about this one?
1 Attachment
what about it? what do you want to find? and what are you given?
Oh. Lol. Forgot.\ AB is a diameter and AB is perpendicular to CD.
alright so that's all the given info?
I know the angles are all 90 degrees.
what do you need to find exactly?
Find BD for AC= 58 DEGREES
AC is a segment, not an angle
Okay..
so is it ACP or ACB that's 58 degrees
This is exactly what it says. Find m BD for m AC= 58 degrees.
oh arc AC, gotcha
angle APC = (1/2)*(arc AC + arc BD) 90 = (1/2)*(58 + x) 90*2 = 58 + x 180 = 58 + x solve for x
122
yep

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