Question

please solve this question it's very important to me​

Answer 1

Step-by-step explanation:

From ∆ APQ

PQ || MN and AM = PM

now, according to the rule of Thales

AM / PM = AN / QN

or, AN / QN = 1 [ as, AM = PM ]

so, AN = QN ................................................ (¡)

From ∆ ABC

BC || PQ and 2×BP = AP [ as, AM=MP=PB ]

now, according to the rule of Thales

AP / BP = AQ / CQ

or, 2×BP / BP = AQ / CQ

or, AQ / CQ = 2

or, AQ = 2×CQ

or, AN + QN = 2×CQ

or, 2×QN = 2×CQ [ From (¡) ]

so, QN = CQ ................................................. (¡¡)

now,

get from (¡) and (¡¡)

AN = QN = CQ

That mean , MN and PQ trisect AC.

(Proved)