## Sunshine447 3 years ago 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!

1. Sunshine447

@phi

2. CliffSedge

A circle inscribed in a triangle?

3. Sunshine447

I guess so

4. CliffSedge

Like this? |dw:1349651230207:dw|

5. Sunshine447

yeah

6. Sunshine447

@CliffSedge yeah, that's what the lesson shows

7. MrMoose

|dw:1349651442977:dw|

8. MrMoose

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

9. Sunshine447

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

10. Sunshine447

@MrMoose

11. MrMoose

to do what?

12. CliffSedge

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

13. Sunshine447

to make the inscribed circle

14. Sunshine447

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

15. CliffSedge

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

16. Sunshine447

angle bisectors?

17. Sunshine447

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

18. MrMoose

|dw:1349651716141:dw|

19. MrMoose

I guess so

20. Sunshine447

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

21. Sunshine447

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.

22. MrMoose

What do you need help with?

23. CliffSedge

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

24. MrMoose

I am unsure as to how I can help

25. Dido525

|dw:1349651958633:dw|

26. Dido525

I guess it's like that.

27. Sunshine447

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

28. Sunshine447

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.

29. Dido525

|dw:1349652171056:dw|

30. Dido525

Like that I guess...

31. Sunshine447

32. CliffSedge

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

33. Dido525

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

34. Dido525

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

35. 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"

36. Dido525

|dw:1349652319786:dw|

37. Dido525

Like that then I suppose?

38. CliffSedge

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

39. phi

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

40. Sunshine447

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

41. phi
42. Sunshine447

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

43. Sunshine447

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.

44. 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

45. Sunshine447

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

46. 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.

47. phi

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

48. Sunshine447

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

49. Sunshine447

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.

50. 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.

51. 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

52. Sunshine447

thanks!

53. 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.