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

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Manager
Joined: 01 May 2016
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Location: United States
GPA: 3.8
If ∠ D C B is a right angle, then A C = [#permalink]

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11 Feb 2018, 21:16
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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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TD

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Joined: 26 Feb 2016
Posts: 2557
Location: India
GPA: 3.12
If ∠ D C B is a right angle, then A C = [#permalink]

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11 Feb 2018, 21:50
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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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If ∠ D C B is a right angle, then A C =   [#permalink] 11 Feb 2018, 21:50
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