# Math

posted by .

I have a question my brother asked me but I need a math expert.

You have two interlocking circles and the radius of circle B goes through the center of circle A and of course the radius of circle A goes through the center of circle B. The radius of each circle is 30 feet. Now, if you draw a line C from the top center of circle A across to the top center of circle B, the line would be 60 feet long and would leave an area below it created by the line C and part of an arc of circle A and part of an arc of circle B. Please give me the area of that space in square feet or the formula for how it's worked. Thanks.

• Math -

We will describe the problem as follows.

Two circles A,B of equal radii (r=30') are centred at P, Q, distance r apart.

Points R and S on circles A, B are such that RS form a common tangent to both circles. Hence PRSQ form a square of side r.

Arcs are drawn with centre P and Q, radius r, which intersect at point D inside the square.

Hence Δ PDQ is an equilateral triangle of side r.

The required area bounded by the side RS , arcs RD and DS will be equal to

Area of square PRSQ - Area of ΔADQ - area of sector RPD - Area of sector SQD.

Note that sectors RPD and SQD have centrai angles of (90-60)=30°.

• Math -

Typo corrections:

Area of square PRSQ - Area of ΔPDQ - area of sector RPD - Area of sector SQD.

Note that sectors RPD and SQD have central angles of (90-60)=30°.

• Math -

Many thanks.

• Math :) -

You're welcome!

## Similar Questions

1. ### math

the number of noncollinear points needed to determine a circle Two. The location of the center, and one point on the circle (ie, the length of radius), you have determined the circle. However, the circle thus determined can be an an …
2. ### Pre-Calc

Describe the conditions necessary for the two circles, where circle a has a larger radius than circle b, to have no points of intersection, while each circle is entirely in the exterior of the other circle.
3. ### Pre-Calc (Circles)

Describe the conditions necessary, where circle A has a larger radius than circle B, for the two circle to have no points of intersection, while circle B is entirely in the interior of circle A.
4. ### Math

Circle C has radius 4 inches. Circle D had radius 9 inches. These two circles are connected. Point A,B,and E are points of tangency. Find AB. From point C to point D(which is the radius of circle C plus the raduis of circle D) it is …
5. ### math gre question

in an infinite series of circles the radius of the second circle is one half the radius of the first circle and the radius of the third circle is one half the radius of the second circle. if the first circle has a radius of one inch …

Two circles of different sizes are tangent at T. A is on the smaller circle, whereas B is on the larger one. Also, segment CD is tangent to the smaller circle, and crosses the goes through the larger circle and hits the other side …
7. ### GEOMETRY(CIRCLE)

Three circles with different radii have their centers on a line. The two smaller circles are inside the largest circle, and each circle is tangent to the other two. The radius of the largest circle is 10 meters. Together the area of …