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Triangle ABC Is an equilateral triangle with it's sides equal to 6a units. AX is a line parallel to line BC. P is a point on AX. From point P a line drawn to intersect AB, AC, BC produced in a point Q,R,S respectively. If PQ=QR=RS then find the length of BR.

Asked by Ram 25th December 2017, 7:48 PM
Answered by Expert
Answer:
begin mathsize 16px style keep space the space vertex space straight B space at space left parenthesis 0 comma 0 right parenthesis
also space BC thin space side space will space concide space with space straight x space axis
So space we space can space find space straight C comma straight A..... equilateral space tirangle space with space side space 6 straight a
Now space PQ equals QR equals RT
triangle PAR space tilde increment TCR
straight A space straight A space test space space AX parallel to CT comma AC space transversal
PR over TR equals 2 over 1 equals AR over RC
so space point space straight R space dvides space AC space in space ratio space 2 colon 1
open parentheses 3 straight a comma 3 straight a square root of 3 close parentheses _________ left parenthesis straight x comma straight y right parenthesis __________ open parentheses 6 straight a comma 0 close parentheses
straight x equals fraction numerator 12 straight a plus 3 straight a over denominator 3 end fraction equals 5 straight a
straight y equals fraction numerator 3 straight a square root of 3 plus 0 over denominator 3 end fraction equals straight a square root of 3
so space point space is open parentheses 5 straight a comma straight a square root of 3 close parentheses
so space distance space between space it space and space left parenthesis 0 comma 0 right parenthesis space is space BR
so space by space distance space formula
BR equals 2 straight a square root of 7 end style
Answered by Expert 10th January 2018, 1:17 PM
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