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# Point C is on AC such that AX=3CX. If ABC=BXA=90°, then what is BX?

+10
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+1771

Point C is on AC such that AX=3CX. If ABC=BXA=90°, then what is BX?

Mellie  Nov 12, 2015

#1
+82721
+10

[ I think this is supposed to read..."Point X  is on AC such that......." ]

Triangle AXB ≈ Triangle BXC

AX/XB ≈ BX/XC

AX*XC  = XB*BX

AX*CX  = BX^2

(3CX)CX  = BX^2

3CX^2  = BX^2

sqrt(3)CX  = BX

Here's the pic :

CPhill  Nov 13, 2015
edited by CPhill  Nov 13, 2015
Sort:

#1
+82721
+10

[ I think this is supposed to read..."Point X  is on AC such that......." ]

Triangle AXB ≈ Triangle BXC

AX/XB ≈ BX/XC

AX*XC  = XB*BX

AX*CX  = BX^2

(3CX)CX  = BX^2

3CX^2  = BX^2

sqrt(3)CX  = BX

Here's the pic :

CPhill  Nov 13, 2015
edited by CPhill  Nov 13, 2015

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