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Question Number 4409 by Rasheed Soomro last updated on 22/Jan/16

Divide a circle into two congruent  regions such that they have no   straightedge.

$$\mathcal{D}{ivide}\:{a}\:{circle}\:{into}\:{two}\:{congruent} \\ $$$${regions}\:{such}\:{that}\:{they}\:{have}\:{no}\: \\ $$$${straightedge}. \\ $$

Commented by prakash jain last updated on 22/Jan/16

Circle with center O.  Draw diameter AOB.  O_1  mid point of AO  O_2  mid point of OB  Draw semicircle with radius AO_1 .  Draw semicircle with radius BO_2  on side.

$$\mathrm{Circle}\:\mathrm{with}\:\mathrm{center}\:\mathrm{O}. \\ $$$$\mathrm{Draw}\:\mathrm{diameter}\:\mathrm{AOB}. \\ $$$$\mathrm{O}_{\mathrm{1}} \:\mathrm{mid}\:\mathrm{point}\:\mathrm{of}\:\mathrm{AO} \\ $$$$\mathrm{O}_{\mathrm{2}} \:\mathrm{mid}\:\mathrm{point}\:\mathrm{of}\:\mathrm{OB} \\ $$$$\mathrm{Draw}\:\mathrm{semicircle}\:\mathrm{with}\:\mathrm{radius}\:\mathrm{AO}_{\mathrm{1}} . \\ $$$$\mathrm{Draw}\:\mathrm{semicircle}\:\mathrm{with}\:\mathrm{radius}\:\mathrm{BO}_{\mathrm{2}} \:\mathrm{on}\:\mathrm{side}. \\ $$

Answered by Rasheed Soomro last updated on 23/Jan/16

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