1. Consider the followingsituation: A circle of with center O(0,0), radius 10m, is inscribed in asquare. The ray of angle 30O, in standard position, intersects thecircle at point B, and continues tointersect the square at point C. LetA denote (10,0). (i) Sketchthe figure indicated in the above description.(ii) Findthe exact coordinates of A, B, and C, and label them on your sketch.(iii) Nowsuppose we have arbitrary acute angle Q (inradians, instead of the 30O). Again draw the sketch!(iv) Againfigure out the exact coordinates of A, B,and C and label them on your sketch.NB: You will use trig functions here!(v) Nowfigure out the equation you would have to solve to find Q to makethe area of ABCA exactly equal to thearea of the sector. HINT: This meansarea of sector is half area of triangle. (You cannot solve such an equationexactly – this is an example of a TRANSCENDENTAL equation, so the theorems ofalgebra do not apply.)

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