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A semicircular paper is folded along a chord such that the folded circular arc is tangent to the diameter of the semicircle. The radius of the semicircle is 4 units and the point of tangency divides the diameter in the ratio 7: 1 . If the length of the crease (the dotted line segment in the figure) is I then determine P^2 .

Correct answer

39

Step-by-step solution

If we complete the circle on arc A Q B , we get the centre O ₂ and radius 4 . Clearly O₁ O₂=5 O₁ A O₂ is isosceles, then aligned A D & = 4^2- ( 5 2 )^2 & = 64-25 2 aligned So A B= 39

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