Question

In triangle ABC, P is a midpoint of BC, Q is a midpoint of AP. If BQ is produced to meet AC at R, prove that RA = 1/3 AC.

Answer 1

★ GEOMETRIC TRIANGLES ★

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To Prove :-

$RA = \frac{1}{3} AC$

Construction :-

Draw PS parallel to BR to meet AC at S.

Proof :-

In Δ BCR, P is the mid-point of BC and PS is parallel to BR.

Where, S is the mid-point of CR
So, $CS = SR$  ----- (1)

Again, In Δ APS, Q is the mid-point of AP and QR  is parallel to PS.

Where, R is the mid-point of AS.
So, $AR = RS$   ----- (2)

From equations (1) and (2),

We get, AR = RS = SC

⇒ $AC = AR + RS + SC$
⇒ $AC = AR + AR + AR$
⇒ $AC = 3AR$

∴ $AR= \frac{1}{3} AC$

--Please refer to the attached image for clarification of diagram and points--
--Please take into consideration another method attached in the form of an image--

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#ExoticExplorer

Answer 2

Answer:

Step-by-step explanation: