Math Is Fun Forum

The graph of the equation

is a circle. Find the radius of the circle. is the radius

OPQRSTUVWX is a regular decagon. A rotation of

degrees about U maps X to R. Given

, find

Two lines

and m intersect at O at an angle of

. Let A be a point inside the acute angle formed by

and m. Let B and C be the reflections of A in lines

and m, respectively. Find the number of degrees in

.

Equilateral triangle ABC has centroid G. Triangle A'B'C' is the image of triangle ABC upon a dilation with center G and scale factor -2/3. Let K be the area of the region that is within both triangles. Find K/[ABC].

The two bases of a right conical frustum have radii 12 and 9. The two bases are 4 units apart. Let the volume of the frustum be V cubic units and the total surface area of the frustrum be A square units. Find V + A.

A

circular sector with radius 15 is rolled to form a cone. Find the volume of the cone.

Let  ABCDEFGH be a rectangular prism, as shown. The areas of faces ABCD, ABFE, and ADHE  are 56, 110, and 385, respectively. Find the volume of the rectangular prism.

The total area of all the faces of a rectangular prism is 22, and the total length of all its edges is 24. Find the length of the internal diagonal of the prism.

In the adjoining figure,  AB is tangent at  A to the circle with center O , point D is interior to the circle, and DB intersects the circle at C. If BC = DC = 3,OD = 2 , and AB = 6, then find the radius of the circle.

i need help with some tangent/circle problems

Two circles have the same center. A chord of the larger circle is tangent to the smaller circle. If the length of the chord is 12, then find the area of the region inside the larger circle but outside the smaller circle.

The circular table in the diagram is pushed tangent to two perpendicular walls. The distances from  on the circumference to the two walls are 27 and 6. What is the radius of the table?

Given regular pentagon ABCDE , a circle can be drawn that is tangent to DC at D and to AB at A. What is the number of degrees in minor arc AD?

Points B and A are on a circle with center at O, and point P is outside the circle such that PA and PB are tangent to the circle. Find AB if PA=12 and the radius of the circle is 9.