XAT 2020 Geometry & Mensuration Question (Hard)

Question

In the figure given below, the circle has a chord AB of length 12 cm, which makes an angle of 60 at the center of the circle, O. ABCD, as shown in the diagram, is a rectangle. OQ is the perpendicular bisector of AB, intersecting the chord AB at P, the arc AB at M and CD at Q. OM MQ. The area of the

Optima Learn · Accepted Answer

Chord AB has length 12 cm and subtends 60 at the centre O. For a chord of length 2R sin 2 , we have 12 2R sin 30 2R 1 2 R, so the radius is R 12 cm. Let the circle be centred at the origin with OA at 30 and OB at 30 . Then A 6 3, 6 , B 6 3, 6 . The midpoint P of AB is 6 3, 0 . The perpendicular bise

XAT 2020 Geometry & Mensuration — Previous Year Question

XAT 2020

Quantitative

Geometry & Mensuration

Hard

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