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Geometry and Measurement Videos 88 videos

SAT Math 1.1 Geometry and Measurement
719 Views

SAT Math 1.1 Geometry and Measurement. What is the circumference of the circle?

SAT Math 1.2 Geometry and Measurement
246 Views

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
267 Views

SAT Math 2.3 Geometry and Measurement. Find the length of AB.

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SAT Math: Working with Chord Lengths to Find the Radius of a Circle 3 Views


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Description:

In the circle above, the point A, which is in the middle of the chord, is 7 inches from the center of the circle. The length of the chord is 10 inches. What is the radius of the circle in inches? Round your answer to one decimal place.


Transcript

00:00

Yeah Whoa Okay Shh Trig shmoop er's Got a circle

00:06

in a line You gotta dot We got a letter

00:09

That's about it in circle above the point eh Which

00:11

is in the middle The cord is seven inches from

00:13

the center of the circle with length of the court

00:16

is ten inches And that's ten inches from there to

00:18

there What's the radius of the circle in inches Run

00:22

your answer thereto One decimal place Okay so let's think

00:26

about this Well this type of cord has nothing to

00:29

do with the pleasant sounding music Like that's a chord

00:32

It's a line drawn on the edges of a circle

00:35

but it will help us find the length of the

00:38

radius How you ask Oh will answer for no extra

00:41

charge The problem says that a is seven inches from

00:44

the center of the circle Well that's rotate the circle

00:47

Teo make things a little easier It looks like that

00:50

Well the line from a to the centre is and

00:52

well perfectly vertical And that cord is perfectly horizontal so

00:57

they form a nice right triangle right there Well this

01:00

happens any time we create a line from the centre

01:02

to the midpoint of accord any cord right And we're

01:05

also going to note that it bisects the cord right

01:08

there So we got five on either side and now

01:11

we've got seven They're in a five They're in a

01:14

right triangle This is getting easier Well the radius is

01:17

actually the high Parton's of this right triangle And the

01:20

problem's states that the cord is ten inches long and

01:22

then point a's and centers We got five inches There

01:25

goes like seven inches So Noel let's use the Pythagorean

01:28

theorem It was his best serum the serum on how

01:32

to make a smoothie not so popular but this one

01:34

was good So we have five squared plus seven squared

01:37

equals R squared now twenty five plus forty nine or

01:40

seventy for is R squared So our is the square

01:42

root of seventy four It's about eight point six Well

01:44

the radius of the circle is about eight point six

01:47

inches Hearing that we've answered this cord problem frankly is 00:01:51.29 --> [endTime] music to our ears

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