InterviewSolution
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InterviewSolution
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If I_(1), I_(2), I_(3) are the centers of escribed circles of Delta ABC, show that the area of Delta I_(1) I_(2) I_(3) is (abc)/(2r) |
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Answer» Solution :AREA `= (I_(1) I_(2) xx I_(3)I_(2) xx I_(1) I_(3))/(4R')` where R' = Circumradius of `Delta I_(1) I_(2) I_(3)` `= ((4R cos.(A)/(2)) (4R cos.(B)/(2))(4R cos.(C)/(2)))/(8R)`(`:' Delta ABC` is pedal TRIANGLE for `Delta I_(1), I_(2), I_(3)`) `=8R^(2) cos.(A)/(2) cos.(B)/(2) cos.(C)/(2)` `= (R^(2) sin A sin B sin C)/(sin.(A)/(2) sin.(B)/(2) sin.(C)/(2))` `= (R^(2) abc)/(8R^(3) sin.(A)/(2) sin.(B)/(2) sin.(C)/(2))` `= (abc)/(2(4R sin.(A)/(2) sin.(B)/(2) sin.(C)/(2)))` `= (abc)/(2r)` |
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