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Let A_(1), A_(2)………A_(26) be a regular polygon with 26 sides inscribed in a circle of radius R. Now A_(1)^('), A_(7)^('), A_(g)^('), be the projections of the orthocentre H ot /_\A_(1)A_(7)A_(9) onto sides A_(7)A_(9), A_(1)A_(9), A_(1)A_(7) respectively. Then |
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Answer» `HA_(1)^(')-HA_(7)^(')+HA_(9)^(')=(2R)/3` `HA_(7)^(')=-2RcosA_(1)cosA_(7)` `HA_(9)^(')=-2RcosA_(1)cosA_(7)` `/_A_(1)=(pi)/13, /_A_(7)=(9pi)/13, /_A_(9)=(3pi)/13` so USING, we get `HA_(1)^(')-HA_(7)^(')+HA_(9)^(')=R/2` |
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