Question

P,Q,R are, respectively, the mid points of sides AB, BC and CA and of a triangle ABC. PR and AQ meet at
X. BR and PQ meet at Y. Prove that XY = 1/4 AB.​

Answer 1

Answer:

$\huge\bf\mathfrak{HOPE..ITS.. HELPS.. }$

Answer 2

Hey

here is your answer

Given : P, Q and R are mid-points in triangle ABC.

Given : P, Q and R are mid-points in triangle ABC.To prove : XY = 1 AB / 4

/ 4 Proof : Since P,Q and R are mid points so

/ 4 Proof : Since P,Q and R are mid points so QR || BC => QR || BP

/ 4 Proof : Since P,Q and R are mid points so QR || BC => QR || BPPQ || AB => PQ || BR

/ 4 Proof : Since P,Q and R are mid points so QR || BC => QR || BPPQ || AB => PQ || BRHence, BPQR is parallelogram.

/ 4 Proof : Since P,Q and R are mid points so QR || BC => QR || BPPQ || AB => PQ || BRHence, BPQR is parallelogram.As diagonals of parallelogram bisect each other, so BX = XQ. Hence, X is mid-point on BQ.

/ 4 Proof : Since P,Q and R are mid points so QR || BC => QR || BPPQ || AB => PQ || BRHence, BPQR is parallelogram.As diagonals of parallelogram bisect each other, so BX = XQ. Hence, X is mid-point on BQ.Similarily, PCQR is parallelogram.

/ 4 Proof : Since P,Q and R are mid points so QR || BC => QR || BPPQ || AB => PQ || BRHence, BPQR is parallelogram.As diagonals of parallelogram bisect each other, so BX = XQ. Hence, X is mid-point on BQ.Similarily, PCQR is parallelogram.Hence, Y is mid point on RC.

/ 4 Proof : Since P,Q and R are mid points so QR || BC => QR || BPPQ || AB => PQ || BRHence, BPQR is parallelogram.As diagonals of parallelogram bisect each other, so BX = XQ. Hence, X is mid-point on BQ.Similarily, PCQR is parallelogram.Hence, Y is mid point on RC.As, X and Y are midpoints so XY || QR and XY = 1 QR / 2

/ 4 Proof : Since P,Q and R are mid points so QR || BC => QR || BPPQ || AB => PQ || BRHence, BPQR is parallelogram.As diagonals of parallelogram bisect each other, so BX = XQ. Hence, X is mid-point on BQ.Similarily, PCQR is parallelogram.Hence, Y is mid point on RC.As, X and Y are midpoints so XY || QR and XY = 1 QR / 2Moreover, QR || BC ( Q and R are mid-points ). Hence, QR = 1 BC / 2

/ 4 Proof : Since P,Q and R are mid points so QR || BC => QR || BPPQ || AB => PQ || BRHence, BPQR is parallelogram.As diagonals of parallelogram bisect each other, so BX = XQ. Hence, X is mid-point on BQ.Similarily, PCQR is parallelogram.Hence, Y is mid point on RC.As, X and Y are midpoints so XY || QR and XY = 1 QR / 2Moreover, QR || BC ( Q and R are mid-points ). Hence, QR = 1 BC / 2So, XY = 1/2 ( 1 BC / 2 )

/ 4 Proof : Since P,Q and R are mid points so QR || BC => QR || BPPQ || AB => PQ || BRHence, BPQR is parallelogram.As diagonals of parallelogram bisect each other, so BX = XQ. Hence, X is mid-point on BQ.Similarily, PCQR is parallelogram.Hence, Y is mid point on RC.As, X and Y are midpoints so XY || QR and XY = 1 QR / 2Moreover, QR || BC ( Q and R are mid-points ). Hence, QR = 1 BC / 2So, XY = 1/2 ( 1 BC / 2 )XY = 1 AB / 4

hence probed