Question

Please help me understand

Amy and Beth are both working on a construction of a circle inscribed in a triangle. Amy starts by finding the angle bisectors of each angle in the triangle. Beth starts by finding the perpendicular bisectors of each side of the triangle. Whose construction will be correct? What additional steps must be taken to complete the construction of the inscribed circle?

Answer 1

@mathmale @campbell_st @ganeshie8

Answer 2

perhaps you should read this link...

http://www.mathopenref.com/inscribed.html

Answer 3

Okay, i did..

Answer 4

Can you walk me through this? @campbell_st

Answer 5

A carnival ride is in the shape of a wheel with a radius of 25 feet. The wheel has 20 cars attached to the center of the wheel. What is the central angle, arc length, and area of a sector between any two cars? Round answers to the nearest hundredth if applicable. You must show all work and calculations to receive credit

Answer 6

@campbell_st ^^^

Answer 7

ok... so sector angle 1st

360 in a circle...

25 cars...

360/25 =

Answer 8

14.4

Answer 9

the central angle will help to tell you the fraction of the circle you are dealing with

fraction = sector angle
-----------
360


the the arc length = cricumference times fraction

sector area = area of crircle times fraction

Answer 10

so then 14.4/360=0.04

Answer 11

well that makes sense...

arc length

\[l = \frac{14.4}{360} \times 2 \times \pi \times r\]

area of sector

\[a = \frac{14.4}{360} \times \pi \times r^2\]

Answer 12

for arc length i got 6.28

Answer 13

and for area i got a=78.53

Answer 14

oops... misread the question the angle is

360/20 = 18

so the fraction is

18/360

sorry about that

Answer 15

your fine thanks for the patience

Answer 16

so arc length = 7.85 ft

area = 98.17 ft^2

Answer 17

arc length= 5pi/2 and
area= 125pi/4

Answer 18

Yes i got the same answers, what is the next step?

Answer 19

Amy and Beth are both working on a construction of a circle inscribed in a triangle. Amy starts by finding the angle bisectors of each angle in the triangle. Beth starts by finding the perpendicular bisectors of each side of the triangle. Whose construction will be correct? What additional steps must be taken to complete the construction of the inscribed circle?
@mathmale Can you help me please?

Answer 20

Hi, Kendra! Happy to "see" you again on OpenStudy!

I'd suggest you actually draw a couple of triangles on paper, some with 2 or 3 sides equal, others with 3 different sides (and so on), and then, in each case, draw in the perpendicular bisectors of each side. BIG question: Do the perpendicular bisectors meet in ONE point that appears to be the center of the circle?

Next, approximate the angle bisectors (there will be three). Again, determine whether or not the lines that bisect the three angles seem to converge at one point which appears to be the center of the circle.

Bet you'd learn a lot by doing this.