In a `DeltaABC, b = 12` units, c = 5 units and `Delta = 30`sq. units. If d is the distance between vertex A and incentre of the triangle then the value of `d^(2)` is _____
Correct Answer - 8
`AI = r "cosec" (A)/(2) = (Delta)/(s) "cosec" (A)/(2)`
Also, `Delta = (1)/(2) bc sin A`
`rArr 30 = (1)/(2) xx 12 xx 5 xx sin A`
`rArr sin A = 1`
`rArr A = (pi)/(2)`
`:. A^(2) = b^(2) + c^(2)`
`rArr a = 13`
`:. S = (a +b +c)/(2) = 15`
Hence, `AI = 2 sqrt2` units
Correct Answer - A
Given equation of family of lines is
`(2x+y-3)+lambda(x+2y-3) =0, lambda in R.`
The family of lines is concurrent at point of intersection of 2x+y-3 = 0 and...
Correct Answer - B
Let any point on the line `x-y=2` be `C(h,h-2)`. The given area of `DeltaABC` is.
`|(1)/(2)||{:(h,,h-2,,1),(-5,,0,,1),(3,,0,,1):}|=20`
or ` |8(h-2)|=40`
or `h-2=+-5`
or `h=7,-3`
Correct Answer - C
`Delta_(1) = (1)/(2) ra, Delta_(2) = (1)/(2) rb, Delta_(3) = (1)/(2) rc`
Given that `Delta_(1), Delta_(2), Delta_(3)` are in A.P.
Therefore, a, b, c are in A.P....
