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Question Number 111734 by Aina Samuel Temidayo last updated on 04/Sep/20

A chord which is a perpendicular  bisector of radius of length 18cm in a  circle, has length.

$$\mathrm{A}\:\mathrm{chord}\:\mathrm{which}\:\mathrm{is}\:\mathrm{a}\:\mathrm{perpendicular} \\ $$$$\mathrm{bisector}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{length}\:\mathrm{18cm}\:\mathrm{in}\:\mathrm{a} \\ $$$$\mathrm{circle},\:\mathrm{has}\:\mathrm{length}. \\ $$$$ \\ $$

Answered by Rasheed.Sindhi last updated on 04/Sep/20

((c/2))^2 +((r/2))^2 =r^2   ((c/2))^2 +9^2 =18^2   (c/2)=(√(324−81))=9(√3)  c=18(√3)

$$\left(\frac{{c}}{\mathrm{2}}\right)^{\mathrm{2}} +\left(\frac{{r}}{\mathrm{2}}\right)^{\mathrm{2}} ={r}^{\mathrm{2}} \\ $$$$\left(\frac{{c}}{\mathrm{2}}\right)^{\mathrm{2}} +\mathrm{9}^{\mathrm{2}} =\mathrm{18}^{\mathrm{2}} \\ $$$$\frac{{c}}{\mathrm{2}}=\sqrt{\mathrm{324}−\mathrm{81}}=\mathrm{9}\sqrt{\mathrm{3}} \\ $$$${c}=\mathrm{18}\sqrt{\mathrm{3}} \\ $$

Commented by Aina Samuel Temidayo last updated on 04/Sep/20

Diagram please?^

$$\mathrm{Diagram}\:\mathrm{please}\overset{} {?} \\ $$

Commented by prakash jain last updated on 05/Sep/20

Commented by Aina Samuel Temidayo last updated on 05/Sep/20

Please how do you know the chord is  also bisected?

$$\mathrm{Please}\:\mathrm{how}\:\mathrm{do}\:\mathrm{you}\:\mathrm{know}\:\mathrm{the}\:\mathrm{chord}\:\mathrm{is} \\ $$$$\mathrm{also}\:\mathrm{bisected}? \\ $$

Commented by prakash jain last updated on 05/Sep/20

Radius is perpendicular to chord  and perpendicular radius always  bisects chord

$$\mathrm{Radius}\:\mathrm{is}\:\mathrm{perpendicular}\:\mathrm{to}\:\mathrm{chord} \\ $$$$\mathrm{and}\:\mathrm{perpendicular}\:\mathrm{radius}\:\mathrm{always} \\ $$$$\mathrm{bisects}\:\mathrm{chord} \\ $$

Commented by Aina Samuel Temidayo last updated on 05/Sep/20

Ok. Thanks.

$$\mathrm{Ok}.\:\mathrm{Thanks}. \\ $$

Commented by Rasheed.Sindhi last updated on 05/Sep/20

ThanX  prakash sir for help of   a nice diagram etc.

$$\mathcal{T}{han}\mathcal{X}\:\:\boldsymbol{{prakash}}\:\boldsymbol{{sir}}\:{for}\:{help}\:{of} \\ $$$$\:{a}\:{nice}\:{diagram}\:{etc}. \\ $$

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