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January 22nd, 2009, 01:12 AM   #1
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Geometry and Trigo Problems!!! help me solve it...

1. Three circles of radii 11.5 m, 15.0 m, and 22.5 m respectively are tangent to each other externally. Find the angle of the triangle formed by joining the centers of the circles.

2. Two circles of radii 3 and 5 are drawn touching a line at A and B 7 cm apart. If the other common external tangent is drawn and intersects the first at P, find the measure of angle P and the length of PA

3, In the figure below left, ABCD is a square. Arcs AC and BD have centers at D and C, respectively. If each side of square ABCD is 2 units long. What is the length of arc AO?
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January 22nd, 2009, 06:19 AM   #2
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Re: Geometry and Trigo Problems!!! help me solve it...

1. Draw a diagram. You will have a triangle whose sides are known. Use th Law of Cosines then the Law of Sines.

2. Draw a diagram. Let the common point between circle be T, then PA = PB = PT ...tangents, so how long is PB? Extend the radius from B as a diameter which will be 10. You have a right triangle knowing two sides and can find angles.

There are several concepts needed for each. Either you know then or you don't. You should do some research and show your effort.
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January 24th, 2009, 08:18 AM   #3
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Quote:
Originally Posted by sheen_daphne
3. ABCD is a square. Arcs AC and BD have centers at D and C, respectively. If each side of square ABCD is 2 units long. What is the length of arc AO?
If arcs AC and BD intersect at O, triangle OCD is equilateral.
Hence angle ADO = pi/2 - pi/3 = pi/6, and so arc AO = pi/3.
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