Can someone please help me "Inscribed circles to triangles"? I watched a video, but it still doesn't make sense..... The video skips a lot of the steps and I'm not sure why...... Please help me!

- anonymous

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- anonymous

@phi

- anonymous

A circle inscribed in a triangle?

- anonymous

I guess so

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## More answers

- anonymous

Like this?
|dw:1349651230207:dw|

- anonymous

yeah

- anonymous

@CliffSedge yeah, that's what the lesson shows

- anonymous

|dw:1349651442977:dw|

- anonymous

the center of the circle is equidistant from all of the sides

- anonymous

I guess I have to get perp bisectors to do it?

- anonymous

@MrMoose

- anonymous

to do what?

- anonymous

Not bisectors, but yes, you'll need perpendiculars.

- anonymous

to make the inscribed circle

- anonymous

im just reading the lesson and it says bisectors..... im so confused

- anonymous

If you want to make the circle, then you need the intersection of angle bisectors.

- anonymous

angle bisectors?

- anonymous

If I post an assignment can you help me with it specifically?

- anonymous

|dw:1349651716141:dw|

- anonymous

I guess so

- anonymous

there are 7 parts, so ill post them one at a time

- anonymous

One:
Construct a circle and a tangent to the circle using a compass and straightedge. (4 points)
Draw three random points on your paper.
Construct the circle through these three points.
Determine the circle's center.
Construct a tangent to the circle, using one of the original three points as the point of tangency.

- anonymous

What do you need help with?

- anonymous

Oh, you're doing the reverse. You're starting with the circle, then circumscribing a triangle around it.

- anonymous

I am unsure as to how I can help

- anonymous

|dw:1349651958633:dw|

- anonymous

I guess it's like that.

- anonymous

im not really sure, but ill do something like that for part one, thanks! now part 2...

- anonymous

Two:
Construct a circumscribed circle about a regular polygon using a compass and straightedge. (4 points)
Choose a regular polygon from which you will draw a circumscribed circle.
triangle | square | pentagon | hexagon
Construct the circumscribed circle.

- anonymous

|dw:1349652171056:dw|

- anonymous

Like that I guess...

- anonymous

how is the circle made?

- anonymous

"Circumscribed circle" means the circle is on the outside of the polygon.

- anonymous

It says a circle inside any of those polygons. I chose a square.

- anonymous

@CliffSedge . Ahh yes. I get that mixes up a lot.

- phi

This seems pretty easy to follow for a circle in a triangle
http://www.mathsisfun.com/geometry/construct-triangleinscribe.html
notice the instructions below the "action figure"

- anonymous

|dw:1349652319786:dw|

- anonymous

Like that then I suppose?

- anonymous

The radius of the circle is the distance from a vertex of the polygon to the polygon's center.

- phi

For a circle through 3 points
http://www.mathsisfun.com/geometry/construct-circle3pts.html

- anonymous

@phi do you have a link for circumscibing too? that helped sooo much

- phi

http://www.mathsisfun.com/geometry/construct-trianglecircum.html

- anonymous

thanks sooo much @phi can you help me with the next part too?

- anonymous

Three:
Construct an inscribed circle within a regular polygon using a compass and straightedge. (4 points)
Choose a regular polygon from which you will draw an inscribed circle.
Note: The polygon you choose must be different from the polygon you chose in problem 2.
triangle | square | pentagon | hexagon
Construct the inscribed circle.

- phi

I would pick a square, and follow the same instructions as for the triangle. Bisect 2 angles and find the intersection to get the center of the circle.
draw a perpendicular from the center to 1 side of the square to find the radius

- anonymous

Okay, how about Six:
Explain, using complete sentences, how you can determine whether or not a circle may circumscribe a quadrilateral.

- phi

Here is the professional answer:
A quadrilateral is cyclic (i.e. may be inscribed in a circle) if one side subtends congruent angles at the two opposite vertices.

- phi

How about
opposite angles of a cyclic quadrilateral are supplementary (sum to 180ยบ)

- anonymous

okay that makes much more sense lol thanks! Seven:
Explain, using complete sentences, why an inscribed circle will only work within a regular polygon.

- anonymous

And, is there a video for this? Construct a circle and a tangent to the circle using a compass and straightedge. (4 points) Draw three random points on your paper. Construct the circle through these three points. Determine the circle's center. Construct a tangent to the circle, using one of the original three points as the point of tangency.

- phi

Construct a circle and a tangent to the circle using a compass and straightedge.
draw the circle. draw a line from the center through the circle. mark the intersection.
construct a perpendicular to the line through that point.

- phi

Draw three random points on your paper. Construct the circle through these three points.
For a circle through 3 points
http://www.mathsisfun.com/geometry/construct-circle3pts.html

- anonymous

thanks!

- phi

Determine the circle's center. I think you have to do this do construct the circle in the first place.
Construct a tangent to the circle, using one of the original three points as the point of tangency. This is the same problem as the first one:
Construct a circle and a tangent to the circle using a compass and straightedge.

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