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In a `Delta ABC`, the `AM` and `GM` of ex-radii are 8 asnd 4 respectively, then inradius is :A. `3`B. `2`C. `1`D. `(2)/(3)` |
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Answer» Correct Answer - D In a `Delta aBC`, the ………… Given `AM = 8` `GM = 4` and Let `HM = H` We know that, `G^(2)=AH` `implies H = (G^(2))/(A) = (4^(2))/(8) = 2 implies (3)/((1)/(r_(1))+(1)/(r_(2))+(1)/(r_(3))) = 2` `implies (3)/((s-a)/(Delta)+(s-b)/(Delta)+(s-c)/(Delta)) = 2` `implies (3Delta)/(3s-(a+b+c)) = 2 implies (3Delta)/(s) = 2` `implies 3r = 2 implies r = (2)/(3)` |
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