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1) Points R and S are on circle E such that arc RS=50 degrees. Point T is also on circle E, find all possible values of angle RTS.

 

2) ABCD is a square with area 100. Circle O is tangent to all four sides of the square. Diagonal BD meets the circle at X and Y, with X closer to D than to B. Find DX.

 Apr 24, 2020
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1)  If T is on major arc(RS), angle(RTS)  =  ½ · 50o.

     If T is on minor arc(RS), angle(RTS)  =  ½ · 310o.

 

2)  Circle(O) is inscribed in square(ABCD).

      Each side of the square is 10.

      Therefore, using the Pythagorean Theorem, the distance from B to D is  10 · sqrt(2).     

      The diameter of the square is 10; the radius is 5.

      The distance from O to D is 5 · sqrt(2).

      The distance from X to D is  5 · sqrt(2) - 5.

 Apr 24, 2020

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