Question

3. In the figure xx l AC A (OBX) = A (OXYCA) find :- AX : AB C Y​

Answer 1

Answer:

Since XY||AC

In△BXYand△BAC.

∠1=∠2 (corresponding angles)

∠B=∠B (common)

△BXY~△BAC (AA corollary)

ar(△BXY)ar(△BAC)=BX2BA2 (area ratio theorem) ....(1)

But ar(△BXY)=12ar(△ABC) (given)

⇒ar(△BXY)ar(△ABC)=12

from (1) and (2) we get

BX2AB2=12⇒BXAB1√2

⇒AB-AXAB=1√2⇒ABAB-AXAB=1√2

⇒1-AXAB=1√2⇒AXAB=1-1√2=√2-1√2

Hence , AXAB=2-√22