In parallelogram ABCD AB = 6cm, AD = 8cm. Point K lies on side BC and CK = 4cm

In parallelogram ABCD AB = 6cm, AD = 8cm. Point K lies on side BC and CK = 4cm, point F lies on side CD and CF = 3cm. Line segment KF crosses out the diagonal AC at point P. Find AP: PC.

Point F of the CD side is its middle, since the opposite side AB = 6 cm, and CF = 3 cm.

Similarly, point K is the middle of the BC side.

Let’s draw a straight line KН parallel to AB and a straight line FM parallel to AD. These segments divide the parallelogram into four parallelograms of equal size.

AO = CO as half of the AC diagonal. OP = CP as half the diagonal of the parallelogram CFOK.

OP = CP = OC / 2 = AO / 2, and since AO = AC / 2, then CP = AC / 4.

Then AR = AC – AC / 4 = 3 * AC / 4.

The ratio AP / PC = (3 * AC / 4) / (AC / 4) = 3.

Answer: AR / PC = 3/1.

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