# ACT Aspire Math: Calculating the Radius of a Circle Using A Right Triangle

In the diagram shown, C is the center of the circle, D is the midpoint of AB, and AB = 2, while CD = 10.

ACT Aspire | Math |

ACT Aspire Math | Geometry |

Math | Geometry |

Product Type | ACT Aspire |

Test Prep | ACT Aspire ACT Aspire Math |

### Transcript

Whatever We'll be here all night folks The radius of

the circle is the hypothesis of the right triangle cdb

or the congruent right triangle a cd we confined cb

using the pythagorean theorem right c b squared equals c

d squared plus d b squared The problem tells us

that two cd is ten so c d then is

ten over two or five Right So since d is

the midpoint of a b we also know that d

b is five right It's the same well plug these

values in the formula above and that gets us we'll

see b squared is five squared plus five sward or

twenty five plus twenty five or fifty Then we just

take square root of each side and simplify it using

the fact that while fifty is twenty five times too

Right so we got square to fifty Factor out that

twenty five times two We get square root of twenty

five which is five times for it to so that's

it The radius of a circle is five times Where

were you two units The answer is d and we

are done