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.

Guest Apr 24, 2020

#1**+1 **

1) If T is on major arc(RS), angle(RTS) = ½ · 50^{o}.

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

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.

geno3141 Apr 24, 2020