Question

if ∆ABC is similar to ∆AXY,AB/AX=5/3.if XY= 4cm and BY bisects angle XYC,find AY. it's urgent. No spamming.please​

Answer 1

Given : ∆ABC is similar to ∆AXY,AB/AX=5/3.if XY= 4cm and BY bisects angle XYC

To find : AY

Solution:

∆ABC is similar to ∆AXY

=> AB/AX  = BC/XY  = AC/AY

=> BC/XY  = AC/AY = 5/3

=> BC/XY = 5/3

XY = 4

=> BC/4 = 5/3

=> BC = 20/3

∆ABC is similar to ∆AXY

=> XY ║ BC

=> ∠XYB = ∠CBY

BY Bisects ∠XYC

=> ∠XYB = ∠CYB

from both

∠CBY =  ∠CYB

=> in Δ BCY

BC = CY

=> CY = 20/3

Hence AC/AY  = 5/3

=> ( AY + CY)/AY  = 5/3

=> (AY + 20/3)/AY = 5/3

=> 3AY + 20  = 5AY

=> 2AY = 20

=> AY = 10

AY = 10