P IS POINTON AB SUCH THAT AP:PB=4:3 PQ IS PARALLEL TO AC FIND PQ:AC - Maths - Triangles

Question

P IS POINTON AB SUCH THAT AP:PB=4:3 PQ IS PARALLEL TO AC FIND PQ:AC

Vijay Kumar Gupta · Accepted Answer

Consider a △ABC in which P is a point on AB such that AP:PB=4:3Also PQ∥AC
We need to find the ratio PQ:ACThe figure is shown below:

Note that in △BPQ and △BAC    ∠BPQ=∠BAC    corresponding angles as PQ∥AC and BA is transversal   ∠PBQ=∠ABC     Common angleSo it implies that,     △BPQ ~△BAC  By AA similaritySince corresponding sides of similar traingles are proportional
            PBAB=PQACTake reciprocal on both sides
               ABPB=ACPQ      PB+APPB=ACPQ  PBPB+ APPB=ACPQ        1+ APPB=ACPQ           1+ 43=ACPQ    since  APPB= 43   given This implies that,    ACPQ= 3+43              = 73Take reciprocal on both sides to get,     PQAC=37