Math Is Fun Forum

How do you get the height of

? When you split it in half, how to you get the height?

Finally, I finished it. I just drew an extra line from O to DP so it's perpendicular!

Never mind. Don't do number (3) and (2). I already figured it out. It is easy once you use you brain.

(3)

Solve it for x=7

(2) Drawing a line from K to the vertice above J gives a right triangle. Now use multiple Pythagorean Theorems

New problem

Two circles are externally tangent at point

, as shown. Segment

is parallel to common external tangent

. Prove that the distance between the midpoints of

and

is

.

Ok thanks, I managed to solve the problem!

The circle problem. I put in 2, and the answer was incorrect.

For (3), won't you also have to add 144 to whatever number you get adding 1+4+9... because there are also 144 small 1x1 squares in the board too! Just a thought. And, if you know the formula, please tell me. My hands are aching from writing so much and adding so many things together! D:

phrontister's diagram is what it is supposed to look like! Great job!

New Problems!

(a) A soccer ball is constructed using 32 regular polygons with equal side lengths. Twelve of the polygons are pentagons, and the rest are hexagons. A seam is sewn wherever two edges meet. What is the number of seams in the soccer ball?

What??

(b)Two circles of radius 1 are externally tangent at

. Let

and

be diameters of the two circles. From

a tangent is drawn to the circle with diameter

, and from

a parallel tangent is drawn to the circle with diameter

. Find the distance between these two tangent lines.

Need help with these! D:

Ok, no problem!

Need help with this problem:

In triangle ABC,

and

. Let

be the angle bisector of

.

(a) Prove that

.

(b) Let

and let

. Using similar triangles ABC and BCD, write an equation relating x and y.

(c) Write the equation from Part b in terms of

and find r.

(d) Compute

and

using Parts a-c. (Do not use a calculator!)