Question

P is the midpoint of bc and q is the midpoint of ap. If bq when produced feet to ac at r. Prove that r=1/3ca

Answer 1

The altitude to the base of anisosceles triangle bisects the vertexangle. The altitude to the base of anisosceles triangle bisects the base. When the altitude to the base of anisosceles triangle is drawn, two congruent triangles are formed, proven by Hypotenuse - Leg.

Answer 2

Here is your answer ⤵⤵⤵

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,   ----- (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,    ----- (2)

From equations (1) and (2),

We get, AR = RS = SC

⇒ AC = AR+RS+SC

⇒ AC = AR+AR+AR

⇒ AC = 3 AR

=> AR = 1/3 AC

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