Question

Q.13 In figure verify whether F is the mid point of AK​

Answer 1

Given: In ΔABC,P 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 ΔBCR,P is the mid-point of BC and PS∥BR.

∴S is the mid-point of CR

⇒CS=SR…(i)

In ΔAPS,Q is the mid-point of AP and QR∥PS

∴R is the mid-point of AS.

⇒AR=RS…(ii)

From (i) and (ii), we get

AR=RS=SC

⇒AC=AR+RS+SC=3AR

⇒AR=

3

1

AC=

3

1

CA

Hence, proved.