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ACT Aspire Math: Calculating the Radius of a Circle Using A Right Triangle 0 Views
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Description:
In the diagram shown, C is the center of the circle, D is the midpoint of AB, and AB = 2, while CD = 10.
Transcript
- 00:03
Okay More shmoop math for you Here we go Circle
- 00:06
time in the diagram shown sees center of the circle
- 00:09
These the mid point a b and a b is
- 00:11
too While cd that thing is ten Well what is
- 00:15
the radius of the circle Time to get rad radius
Full Transcript
- 00:22
Whatever We'll be here all night folks The radius of
- 00:24
the circle is the hypothesis of the right triangle cdb
- 00:28
or the congruent right triangle a cd we confined cb
- 00:32
using the pythagorean theorem right c b squared equals c
- 00:36
d squared plus d b squared The problem tells us
- 00:40
that two cd is ten so c d then is
- 00:44
ten over two or five Right So since d is
- 00:46
the midpoint of a b we also know that d
- 00:49
b is five right It's the same well plug these
- 00:52
values in the formula above and that gets us we'll
- 00:55
see b squared is five squared plus five sward or
- 00:57
twenty five plus twenty five or fifty Then we just
- 01:00
take square root of each side and simplify it using
- 01:03
the fact that while fifty is twenty five times too
- 01:05
Right so we got square to fifty Factor out that
- 01:07
twenty five times two We get square root of twenty
- 01:10
five which is five times for it to so that's
- 01:13
it The radius of a circle is five times Where
- 01:15
were you two units The answer is d and we
- 01:18
are done
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