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SAT Math: Finding the Area of a Circle's Shaded Region Using Tangential Lines and Proportions 17 Views


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Description:

In the circle above, B is the center of the circle and AC is tangent to the circle. If the radius of this circle is 4, what is the area of the shaded region? Round your answer to one decimal place.


Transcript

00:00

Yeah Whoa Okay set match members got a circle here

00:06

and it looks like a non forty five forty five

00:10

ninety trying because you've got thirty five they're OK in

00:12

the circle B is the center of the circle and

00:15

a C'est tangent to the circle If the radius of

00:18

this circle is for what is the area of the

00:21

shaded regions are around you're running short on this place

00:27

Okay so when the lines change into a circle it

00:29

means that it only intersex circle at one measly point

00:32

right there Special thing about tangent lines and circles though

00:35

is that they form right angles with the radius line

00:39

that they intersect Well that lucky angle is a right

00:42

there That's ninety degrees So if we know that and

00:45

we know the thirty five degree angle there then we

00:47

know the fifty five degree angle is right They're right

00:50

We got one eighty minus any money right So well

00:53

to find out what proportion of the circle is shady

00:56

use angle B and compare it to the full three

00:59

sixty degrees The non shaded region is fifty five degrees

01:03

right there so we're just going to subtract that amount

01:05

from the three Sixty to find degrees of the big

01:08

region which is well three Sixteen minus fifty five That's

01:11

three Oh five and there's a bit more calculating to

01:14

Dio We need to find the area and thankfully this

01:17

problem was kind enough to provide the radius So formula

01:21

for the area of a circle is pi r squared

01:24

Right So we got pie four squared or sixteen pie

01:27

And here's the proportion that shows the area of that

01:29

shaded region with access the area So it's three Oh

01:32

five is tow three sixty as axes to sixteen pie

01:36

Well if we multiply it out we get three Oh

01:38

five times that he has sixteen there and that's fifteen

01:41

thousand three hundred thirty one almost dish And that's three

01:45

sixty x They're so Acts here is 42 point six

01:49

The area of the shaded regions The part that looks

01:51

like you know Pac Man eating a lemon wedge is

01:54

forty two point six Yeah they don't give us units 00:01:56.55 --> [endTime] No whatever

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