1. In the given figure. ABC is a triangle in which. AB = 10 cm. AC = 6 cm and altitude AE = 4 cm. If AD is the diameter of the circum-circle. then what is the length (in cm) of circum-radius?
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By: anil on 05 May 2019 01.47 am
Given : AB = 10 cm. AC = 6 cm and altitude AE = 4 cm To find : Circumradius = $$R$$ = ? Solution : In $$ riangle$$ ACE, => $$(CE)^2=(AC)^2-(AE)^2$$ => $$(CE)^2=(6)^2-(4)^2$$ => $$(CE)^2=36-16=20$$ => $$CE=sqrt{20}$$ cm Similarly, $$BE = sqrt{100-16}=sqrt{84}$$ cm Now, BC = BE+CE = $$(sqrt{20}+sqrt{84})$$ cm Area of $$ riangle$$ ABC = $$frac{1}{2} imes(AE) imes(BC)$$ => $$ riangle=frac{1}{2} imes4 imes(sqrt{20}+sqrt{84})$$ => $$ riangle=2(sqrt{20}+sqrt{84})$$ $$cm^2$$ $$ herefore$$ Circumradius, $$R=frac{abc}{4 riangle}$$ = $$frac{10 imes6 imes(sqrt{20}+sqrt{84})}{4 imes2(sqrt{20}+sqrt{84})}$$ = $$frac{60}{8}=7.5$$ cm => Ans - (B)
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