1. In the given figure. PR and ST are perpendicular to tangent QR. PQ passes through centre 0 of the circle whose diameter is 10 cm. If PR = 9 cm. then what is the length (in cm) of ST?
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By: anil on 05 May 2019 01.48 am
Given : PR = 9 cm and radius OM = PO = OS = 5 cm To find : ST = $$x$$ = ? Solution : Let SQ = $$y$$ cm In $$ riangle$$ PRQ and $$ riangle$$ OMQ => $$angle$$ PRQ = $$angle$$ OMQ = $$90^circ$$ and $$angle$$ PQR = $$angle$$ OQM (common angle) => $$ riangle$$ PRQ $$sim$$ $$ riangle$$ OMQ => $$frac{PR}{PQ}=frac{OM}{OQ}$$ => $$frac{9}{10+y}=frac{5}{5+y}$$ => $$45+9y=50+5y$$ => $$9y-5y=50-45$$ => $$y=frac{5}{4}$$ -------------(i) Similarly, in $$ riangle$$ PRQ and $$ riangle$$ STQ => $$frac{PR}{PQ}=frac{ST}{SQ}$$ => $$frac{9}{10+y}=frac{x}{y}$$ => $$9y=10x+xy$$ => $$9 imesfrac{5}{4}=x(10+frac{5}{4})$$ => $$frac{45}{4}=xfrac{45}{4}$$ => $$x=ST=1$$ cm => Ans - (A)
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