KVPY Government Jobs Exams

A circle is drawn in a sector of a larger circle of radius r, as shown in the adjacent figure. The smaller circle is
tangent to the two bounding radii and the arc of the sector. The radius of the small circle is

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KVPY Other Question
A regular octagon is formed by cutting congruent isosceles right- angled triangles from the corners of a square. If
the square has side- length 1, the side - length of the octagon is Suppose Q is a point on the circle with centre P and radius 1, as shown in the figure ; R is a point outside the circle such that QR = 1 and QRP = 2 degree. Let S be the point where the segment RP intersects the given circle. Then measure of RQS equals