Required is the Perimeter of the 2 sides of the triangle+3/4permeter of the circle.
3/4 Perimeter of the circle = 3/4*2*Pie*2 (radius, r=2)
= 3 Pie
Now to find the sides of the triangle, we should know the base.
To find the base, the attached pic may be helpful. As the radii form a right anbgle at the center, the triangle inside the circle is an isocsles triangle with sides = 2 (radius)
By Pythogoreon Theorem Base = 2* sqrt (2)
We have the base and height (5)
Again by Pythogoreon theorem
Side = sqrt (25 + 2) [Notice that we have to consider 1/2 of the base]
Hence, total req perimeter = 3+2*3sqrt(3)
= 3+6*sqrt(3) [2 represents for two sides]
Hope this helps.
Can you please explain how is the triangle a right angled isoceles triangle? Please see the text in red above
You know that:
Circumference = 2 x Pi x r
If r is constant, we can conclude that circumference (or length of sector) is proportional to its angle (= 360 degrees).
Therefore; (Length of sector) α
(angle of the sector)
S1/S2 = Angle1/Angle2
We can use this knowledge to find any angle if we know the length sector of the circle and we know the length of the circumference.
From the picture, the circumference = 2 x Pi x 2 = 4Pi
and the top sector on the ice cream has length = (3/4) x 4 Pi = 3Pi
The length of the sector under the triangle that you questioned = 4Pi - 3Pi = Pi
Put all info into the equation that I set above.
S1 = Pi
S2 = Circumference of the circle = 4Pi
Angle1 = what we want to know
Angle2 = 360 (Angle of the circumference)
Pi/4Pi = Angle1/360
Angle1 = 360 x 1/4 = 90 degrees
Or you can use this equation to find the angle of any sector
Length of sector = Angle of the sector x radius
S = @r
Pi = @ x 2
@ = Pi/2
We know that Pi/2 is 90 degrees.