Question

The sides
AB
,
BC
, and
AC
of a △ABC are tangent to a circle at points P, Q, and R respectively. Find AP, PB, BQ, QC, CR, and RA if AB = 10 cm, BC = 12 cm, and CA = 5 cm.

Answer 1

Given :  AB , BC & AC sides of triangle are tangents to circle at P , Q & R .AB = 10 cm, BC = 12 cm, and CA = 5 cm.

To find : AP, PB, BQ, QC, CR, and RA

Solution:

AB , BC & AC are tangents at P , Q & R

=> AP = AR   = x  ( equal tangents)

   BP = BQ   = y       ( equal tangents)

   CQ  = CR   =  z    ( equal tangents)

AB = AP  +  BP

=> x + y  = 10

BC = BQ + QC

=> y  + z  = 12

AC = AR + CR

=>  x  + z   =  5

Adding all

=> 2(x + y + z)  = 10 + 12 + 5

=> x + y + z  = 13.5

x + y + z - (x + y)  =  13.5 - 10  => z  =  3.5

x + y + z - (z + y)  =  13.5 - 12  => x  =  1.5

x + y + z - (z + x)  =  13.5 - 5  => y  = 8.5

AP  = AR = 1.5  cm

BP = BQ = 8.5  cm

QC = CR = 3.5 cm

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