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SAT Math 1.1 Geometry and Measurement. What is the circumference of the circle?
SAT Math: Geometry and Measurement Drill 1, Problem 2. If A = (0, 4), B = (-3, 2), and C = (1, 0), which point is in the interior of angle ABC?
SAT Math 2.3 Geometry and Measurement. Find the length of AB.
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
Full Transcript
- 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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