trivikram wrote:

sgoll wrote:

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]

=3sqrt (3)

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

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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.