The famous mathematician associated with finding the sum of first 100 natural numbers is Gauss
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1. In the adjacent figure, AB and CD are common tangents to two circles of unequal radii. Prove that AB = CD.
2. In the figure, a square is inscribed in a circle of diameter 14 cm and another square is circumscribing the circle. Find the ratio of the area of the outer square to the area of the inner square.
3. A number 'x' is chosen from the numbers - 3, - 2, -1, 0, 1, 2. Find the probability that x2 les than equal to 4.
4. If the point (x, y) is equidistant from the points (a - b, a +b) and (- a - b, a + b), prove that x- a = 0.
5. If the roots of the equation (a2 + b2 )x2 - 2(ac + bd)x + (c2 +d2 ) = 0 are equal, then prove that a/b = c/d
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