Question

ABCD is a parallelogram, its diagonals intersect at O . OA =16, OD=13, OB=p+7, OC=p+q, then p and q are ​

Answer 1

Given AC and BD are the diagonals of the parallelogram ABCD.

The points P and Q trisects the diagonal BD

We know that, the diagonals of a parallelogram bisect each other.

∴ AC and BD bisect each other at O.

⇒ OA = OC and OB = OD

Given P and Q trisects the diagonal BD.

∴ BP = PQ = DQ → (1)

Consider, OB = OD

BP + OP = OQ + DQ

DQ + OP = OQ + DQ [From (1)]

∴ OP = OQ

In quadrilateral APCQ diagonals AC and PQ bisect each other

Hence, APCQ is a parallelogram. [Since, if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram]

∴ CQ || AP [Opposite sides of parallelogram].

Answer 2

Question:

ABCD is a parallelogram, its diagonals intersect at O . OA =16, OD=13, OB=p+7, OC=p+q, then p and q are ​

Answer:

OA = 16

OC = p+q

OA = OC (diagonals of paralelogram bisect each other)

OA = p+q = 16

OD = 13

OB = p+7

OD = OB (diagonals of paralelogram bisect each other)

OD = p+7 = 13

p = 13 - 7 = 6

OA = p+q = 16

OA = 6+q = 16

6+q = 16

q = 16-6

q = 10