The sides AB, BC and CA of triangle ABC touch a circle with center O and radius r at P, Q and R respectively.Prove that AB+CQ=AC+BQ and Area(ABC)=1/2(perimeter of ABC)

Asked by Jai Gupta | 21st Feb, 2014, 10:24: AM

Expert Answer:

begin mathsize 16px style From space the space figure comma
AQ equals AR comma space BP equals BQ comma space CP equals CR space space space space Tangents space from space an space exterior space point
AQ equals AR
AB plus BQ equals AC plus CR
AB plus BP equals AC plus CP space space space space space space space space space space space space BQ equals BP space and space CR equals CP
Perimeter space of space increment ABC
AB plus BC plus CA
equals AB plus left parenthesis BP plus PC right parenthesis plus CA
equals AB plus BP plus left parenthesis AC plus PC right parenthesis
equals 2 AB plus 2 BP
equals 2 left parenthesis AB plus BP right parenthesis
equals 2 AQ
equals 1 half cross times Perimeter space of space increment ABC end style

Answered by  | 30th Nov, 2017, 12:44: PM