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If ∠ D C B is a right angle, then A C =

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If ∠ D C B is a right angle, then A C =  [#permalink]

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New post 11 Feb 2018, 20:16
1
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A
B
C
D
E

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  45% (medium)

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66% (01:22) correct 34% (02:30) wrong based on 53 sessions

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If ∠ D C B is a right angle, then A C =

a 7

b 3+3√3

c 8

d 4+3√2

e 3+4√2

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If ∠ D C B is a right angle, then A C =  [#permalink]

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New post 11 Feb 2018, 20:50
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In Triangle DCB(right-angled triangle), \(DB^2 = (4\sqrt{2})^2 + (4\sqrt{2})^2 = 64\) -> DB = \(\sqrt{64} = 8\)

Triangles DXA and AXB are similar(SAS), therefore DX = XB = 4

In Triangle DXA, Side \(AX = \sqrt{5^2 - 4^2} = \sqrt{25 - 16} = \sqrt{9} = 3\)
In Triangle DXC, Side \(XC = \sqrt{(4\sqrt2)^2 - 4^2} = \sqrt{16} = 4\)

Therefore, \(AC = AX + XC = 3+4\) = 7(Option A)

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Re: If ∠ D C B is a right angle, then A C =  [#permalink]

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New post 20 Dec 2018, 13:52
All this the same as pushpitkc, therefore DX = XB = 4

Recognise triangle DXA as a 3, 4, 5 right angle triangle. Therefore AX=3
Recognise triangle DXC as a 45, 45, 90 right angle triangle (angle C has been bisected, X is 90º, so part of D is also 45º). Again, this is a triangle to recognise. Hypotenuse is 4√2, so legs are 4.

4+3=7

These two, plus the 30-60-90 right angle triangle ones that very much should be memorised
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Re: If ∠ D C B is a right angle, then A C = &nbs [#permalink] 20 Dec 2018, 13:52
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If ∠ D C B is a right angle, then A C =

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