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 $P^2$ .

Question

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

.

A semicircular paper is folded along a chord such that the folded circular arc is tangent to the diameter of the

Quantrex Academy · Accepted Answer

Correct answer: 39

If we complete the circle on arc A Q B , we get the centre O_2 and radius 4 . Clearly O_1 O_2=5 Δ O_1 A O_2 is isosceles, then aligned A D & = 4^2-((5)/(2))^2 & = 64-25 2 aligned So A B= 39

A semicircular paper is folded along a chord such that the folded...

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