Question Number 101686 by bemath last updated on 04/Jul/20

Commented bybemath last updated on 05/Jul/20

R = ((abc)/(4L_(ΔABC) )) , s =((13+14+15)/2) = ((42)/2) =21  area ΔABC = (√(21×8×7×6))                              = 7×3×4 = 84  R = ((13×14×15)/(4×84)) = ((13×15)/(24))

Commented bybobhans last updated on 04/Jul/20

translate in english

Commented bybemath last updated on 04/Jul/20

In the figure the outer circle of the triangle abc is drawn if AB = 13, BC = 14 and AC = 15. Find the shortest distance from the center of the circle to AB

Commented bybobhans last updated on 04/Jul/20

d = (√((8.125)^2 −(6.5)^2 )) = (√((8.125+6.5)(8.125−6.5)))  d= (√(14.625×1.625))= 4.875 = ((39)/8)  answer D. (★)

Commented by1549442205 last updated on 05/Jul/20

By above the solution the question mus be  εFind the radius of the circumcircle of   the triangle ABCε.R=((13×15)/(24))  d=(√(R^2 −(((AB)/2))^2 ))=(√((((13×15)/(24)))^2 −((13^2 )/4)))  =(√(((13^2 )/4)×(((15^2 )/(12^2 ))−1)))=((13)/2)(√((15^2 −12^2 )/(12^2 )))  =((13)/(24))(√(81))=((39)/8)