Emily778
Find the value of x.
FG perpendicular to OP, RS perpendicular to OQ, FG=20, RS=24, OP=14



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Emily778
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Emily778
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@Hunus
@jim_thompson5910

jim_thompson5910
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let r = radius of the circle

jim_thompson5910
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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

Emily778
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100 + 196 = 296^2. Now what?

jim_thompson5910
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r^2 = 296
so
r = ???

Emily778
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296


jim_thompson5910
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r^2 is 296, not r

Emily778
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87, 616

jim_thompson5910
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don't square it though

jim_thompson5910
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how do you undo squaring something

Emily778
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sqrt?


Emily778
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16.9?

jim_thompson5910
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you did sqrt(296) right?

Emily778
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Yea

jim_thompson5910
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it's close, but not correct

jim_thompson5910
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sqrt(296) = 17.2046505340852
round to whatever place you need to

Emily778
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17.2 isn't one of the answers. Only 16.9

jim_thompson5910
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but remember, we want x, not r

jim_thompson5910
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we use r to get x

Emily778
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the possible answers are: 16.9, 14, 12.3, and 12..

jim_thompson5910
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\[\large r = \sqrt{296} \rightarrow r^2 = 296\]
\[\large (OQ)^2 + (RQ)^2 = (OR)^2\]
\[\large (OQ)^2 + (RQ)^2 = r^2\]
\[\large x^2 + 12^2 = 296\]
\[\large x^2 + 144 = 296\]
...
...
...
\[\large x = ???\]

Emily778
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152

Emily778
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12.3

jim_thompson5910
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\[\large x^2 = 152\]
so
\[\large x = ???\]

jim_thompson5910
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good, x is roughly 12.3

Emily778
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What about this one?

jim_thompson5910
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what about it? what do you want to find? and what are you given?

Emily778
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Oh. Lol. Forgot.\
AB is a diameter and AB is perpendicular to CD.

jim_thompson5910
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alright so that's all the given info?

Emily778
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I know the angles are all 90 degrees.

jim_thompson5910
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what do you need to find exactly?

Emily778
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Find BD for AC= 58 DEGREES

jim_thompson5910
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AC is a segment, not an angle

Emily778
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Okay..

jim_thompson5910
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so is it ACP or ACB that's 58 degrees

Emily778
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This is exactly what it says.
Find m BD for m AC= 58 degrees.

jim_thompson5910
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oh arc AC, gotcha

jim_thompson5910
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angle APC = (1/2)*(arc AC + arc BD)
90 = (1/2)*(58 + x)
90*2 = 58 + x
180 = 58 + x
solve for x

Emily778
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122
