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Question Number 17886 by b.e.h.i.8.3.417@gmail.com last updated on 11/Jul/17

Commented by b.e.h.i.8.3.417@gmail.com last updated on 12/Jul/17

$$1)circleradius=R$$$$2)acuteanglebetweenchords:AB,CD=\phi$$$$find:{AP}^2+{BP}^2+{CP}^2+{DP}^2.$$$$(intermsof:Rand\phi )$$$$trialcase:$$$$when:\phi ={90}^{\bullet }$$$$\Rightarrow {AP}^2+{BP}^2+{CP}^2+{DP}^2=4R^2$$

Commented by ajfour last updated on 12/Jul/17

$$\mathrm{what}\mathrm{if}\mathrm{the}\mathrm{chord}\mathrm{lengths}\mathrm{have}\mathrm{a}$$$$\mathrm{constant}\mathrm{ratio}\mathbf{k}\mathrm{and}\mathrm{acute}\mathrm{\angle }$$$$\mathrm{between}\mathrm{them}\mathrm{is}\varphi ,\mathrm{with}\mathrm{radius}\mathrm{R}?$$

Commented by mrW1 last updated on 12/Jul/17

Commented by mrW1 last updated on 12/Jul/17

$${AP}^2+{BP}^2+{CP}^2+{DP}^2\mathrm{is}\mathrm{not}\mathrm{constant}$$$$\mathrm{for}\mathrm{a}\mathrm{given}\phi ,\mathrm{so}\mathrm{you}\mathrm{can}\mathrm{not}\mathrm{express}\mathrm{it}$$$$\mathrm{in}\mathrm{terms}\mathrm{of}\mathrm{R}\mathrm{and}\phi .\mathrm{the}\mathrm{case}\phi =90°\mathrm{is}\mathrm{an}$$$$\mathrm{exception}.$$$$\mathrm{See}\mathrm{examples}:$$

Commented by ajfour last updated on 12/Jul/17

$$\mathrm{i}\mathrm{meant}\mathrm{AB}=\mathbf{k}\left(\mathrm{CD}\right).$$

Commented by b.e.h.i.8.3.417@gmail.com last updated on 12/Jul/17

$$mrAjfour!haveyouanysolutionforthiscase?$$

Commented by ajfour last updated on 13/Jul/17

$$\mathrm{i}\mathrm{think}\mathrm{even}\mathrm{in}\mathrm{this}\mathrm{question}\mathrm{will}\mathrm{not}$$$$\mathrm{fetch}\mathrm{unique}\mathrm{answers},\mathrm{given}\varphi ,\mathrm{R},$$$$\mathrm{and}\mathbf{k}.\mathrm{Both}\mathrm{chord}\mathrm{lengths}\mathrm{and}\varphi$$$$\mathrm{and}\mathrm{R}\mathrm{are}\mathrm{required}.\mathrm{See}\mathrm{Q}.17963..$$

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