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#1
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Re: Geomerty question
These types of problems are very simple. Ignore the circle in the beginning. Two properties are used:
1.) Two angles forming a straight angle are supplementary angles. Basically this means when there are two angles side by side on a straight line, they add up to 180 degrees. 2.) The 3 angles on a triangle add up to 180 degrees. The rest is just algebra. Label each relevant angle x, y, z, etc. Write out relationships that you find. Combine equations to show your desired equality. |
#2
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Re: Geomerty question
Using the above 2 relationships, you would first show that blue is equal to green+pink and blue is equal to red plus yellow. Thus b = g+p = r+y. To show b = g+r, you must show p = r (can be seen by substitution).
The last part of the puzzle was pointed out above. You can equate red to pink since they subtend the same chord (the lines forming the angles touch the same 2 points on the circle, and thus the vertex, even if you move it around, as long as it is touching the circle will have the same angle). Plugging in r=p to b=g+p, you get b=g+r. |
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