Question

in the figure PQ parallel to AB, P and Q are the midpoint of AC and BC, AB = 10cm

a) find PQ
b) find ratio of CP : PA And CQ : QB
( please help me solve this problem, i will make you as brainliest ) ​

Answer 1

Answer:

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In given figure, P is the mid-point of BC and Q is the mid-point of AP. If BQ when produced meets AC at R, Prove that RA=

3

1

CA.

1008594

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Solution

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Given A △ABC in which P is the mid-point of BC, Q is the mid-point of BC, Q is the mid-point of AP, such that BQ produced meets AC at R

To prove RA=

3

1

CA

Construction Draw PS||BR, meeting AC at S.

Proof In △BCR, P is the mid-point of BC and PS||BR.

∴ S is the mid−point of CR.

⇒ CS=SR

In △APS, Q is the mid-point of AP and QR||PS.

∴ R is the mid−point of AS

⇒ AR=RS

From (i) and (ii), we get

AR=RS=SC

⇒ AC=AR+RS+SC=3AR

⇒ AR=

3

1

AC=

3

1

CA [Hence proved]

Answer 2

Answer:

We have

( AC AQ )= 93 = 31

( AB AP )= 10.5 3.5 = 31

In ΔAPQ & ΔABC

( AC AQ )=( AB AP)& ∠PAQ=∠BAC

Thus ΔAPQ∼ΔABC by SAS criterion.

Hence ( AC AQ )=( BCPQ ) (by cpst)

⇒ 31=( BC4.5 )

⇒BC=13.5cm.solution