in the given figure, PQR is the incircle of ∆ABC and AB, BC and AC torch the circle at P ,Q and R respectively. if BQ = 8 cm, CQ = 6 CM and the perimeter of ∆ABC is 36 CM, then what is the length of AB in cm ?
a)14
a)8
c)10
d)12
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BQ= BP(tangents from the same point meets circle at equal distance)
QC=CR
AR=AP
now perimeter of triangle ABC= 36
=>AP+BQ+BP+AR+QC+RC=36
so, 2AP+2BQ+2QC= 36
2(AP)+2(8)+2(6)=36
2AP+16+12=36
2AP=36-28
AP=8/2
AP = 4
Now, AB=AP+BP
=4+8
=12cm
QC=CR
AR=AP
now perimeter of triangle ABC= 36
=>AP+BQ+BP+AR+QC+RC=36
so, 2AP+2BQ+2QC= 36
2(AP)+2(8)+2(6)=36
2AP+16+12=36
2AP=36-28
AP=8/2
AP = 4
Now, AB=AP+BP
=4+8
=12cm
Anonymous:
hope u got it
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