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Most Important Selected Qs for JEE AdvancedMathematicsCircle

A semicircle is drawn outwardly on chord A B of the circle with centre O and unit radius. The perpendicular from O to A B meets the semicircle on A B at C . Then length of A B so that O C has maximum length is K . Then K is equal to___

Correct answer

2

Step-by-step solution

Let O D= a and A D= 1- a O C=O D+C D= 1-a O C^2=( a + 1-a )^2=1+2 a(1-a a(1-a) should be maximum at a = 1 2 , the above expression attains maximum value aligned & OD = 1 2 & AD = 1 2 aligned A B=2 A D= 2

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