solid geometry - special triagle

SOURCE:COMPETITION
Number of Problems: 2. : (Book)

 

 

1.
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Six points are equally spaced around a circle of radius 1. Three of these points are the vertices of a triangle that is neither equilateral nor isosceles. What is the area of this triangle? extbf{(A)} frac{sqrt{3}}{3}qquad extbf{(B)} frac{sqrt{3}}{2}qquad extbf{(C)} extbf{1}qquad extbf{(D)} sqrt...

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2.
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In rectangle ABCD, AD=1, P is on overline{AB}, and overline{DB} and overline{DP} trisect angle ADC. What is the perimeter of riangle BDP?

draw((0,2)--(3.4,2)--(3.4,0)--(0,0)--cycle);draw((0,0)--(1.3,2));draw((0,0)--(3.4,2));dot((0,0));dot((0,2));dot((3.4,2));dot(...

mathrm{(A)} 3+frac{sqrt{3}}{3} qquadmathrm{(B)} 2+frac{4sqrt{3}}{3} qquadmathrm{(C)} 2+2sqrt{2} qquadmathrm{(D...

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