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

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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.

Additional Topics in Math | Right triangle trigonometry |

Product Type | SAT Math |

SAT | SAT Math |

SAT Math | Additional Topics in Math Geometry and Measurement |

Test Prep | SAT Math |

### Transcript

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

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

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

about this Well this type of cord has nothing to

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

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

but it will help us find the length of the

radius How you ask Oh will answer for no extra

charge The problem says that a is seven inches from

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

Teo make things a little easier It looks like that

Well the line from a to the centre is and

well perfectly vertical And that cord is perfectly horizontal so

they form a nice right triangle right there Well this

happens any time we create a line from the centre

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

also going to note that it bisects the cord right

there So we got five on either side and now

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

right triangle This is getting easier Well the radius is

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

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

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

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

theorem It was his best serum the serum on how

to make a smoothie not so popular but this one

was good So we have five squared plus seven squared

equals R squared now twenty five plus forty nine or

seventy for is R squared So our is the square

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

the radius of the circle is about eight point six

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