Question

In ΔАВC, the mid-points of the sides BC, CA and AB are P, Q and R respectively. PR and BQ meet at X. CR and PQ meet at Y. Then XY is equal to ______.

पर्याय

• `1/2 BC`

• `1/3 BC`

• `1/4 BC`

• `1/5 BC`

Answer 1

In ΔАВC, the mid-points of the sides BC, CA and AB are P, Q and R respectively. PR and BQ meet at X. CR and PQ meet at Y. Then XY is equal to `underlinebb(1/4 BC)`.

Explanation:

Put BC = 1 and place B = (0, 0), C = (1, 0), A = (0, t) any t ≠ 0.

Midpoints:

`P = (1/2, 0)` 

`Q = (1/2, t/2)` 

`R = (0, t/2)`

Solve for X = PR ∩ BQ

⇒ `X = (1/4, t/4)`

Solve for Y = CR ∩ PQ

→ `Y = (1/2, t/4)`

So, `XY = 1/2 - 1/4 = 1/4` of BC.

Hence, `XY = 1/4 xx BC`.