circle (radians) question (1 Viewer)

[Masaken]

Two circles of radii 3cm and 4cm have their centres 5cm apart. Calculate the area common to both sides correct to 2dp.

need some help on this question please + visualising it

 

[cossine]

Imagine, two circles with there centre on a horizontal line.

Maybe one approach could be to think of the circles as on the euclidean plane. Then use integration.

Edit: Integration not needed. Try something involving (1/2)r^2*theta. See Vali post

 

[Vall]

Here's your visualisation

 

[Masaken]

Imagine, two circles with there centre on a horizontal line.

Maybe one approach could be to think of the circles as on the euclidean plane. Then use integration.

Edit: Integration not needed. Try something involving (1/2)r^2*theta. See Vali post

Yup, then make two triangles from the two points of intersection of the two circles to their centres, but how would you get the area in between + where would you apply the area of a sector formula?

 

[cossine]

Yup, then make two triangles from the two points of intersection of the two circles to their centres, but how would you get the area in between + where would you apply the area of a sector formula?

You use (1/2)*(r^2)*theta - area_of_triangle, to find the area on each side of the chord.