CAT4MBA

After sitting ideally for more than 2 hrs in office w/o any work I thought of creating a complex geometric fig and the result is below. But I guess the questions are easy.

In the given below figure a rectangle XYCD is inscribed in a circle with center at O. AX and AY are two tangents drawn from point an external point A. C is the intersection point of the circle and the line AO.

If XY = 10 cm and ang(BYO)=30 degree then

Q1. What is the length of the tangent AY?
a. 10 cm
b. 10/sqrt(2) cm
c. 10sqrt(2) cm
d. None of the above

Q2. What is the length of the radius of the circle?
a. 10 cm
b. 10/sqrt(2) cm
c. 10sqrt(2) cm
d. None of the above

Q3. What is the area of the region exterior to the circle and bounded by two tangents?
a. 50sqrt(3) – 25(pi-1)
b. 25[sqrt(3) – (pi-1)]
c. 50[sqrt(3) – (pi-1)]
d. None of the above

Q4. What is the length of the line segment AC ?
a. 10/sqrt(3)
b. 10sqrt(3) - 10/sqrt(3)
c. 100 [sqrt(3) - 1 ]
d. None of the above