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# In triangle ABC, we have AC = BC = 7 and AB = 2. Suppose that D is a p

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Math Expert
Joined: 02 Sep 2009
Posts: 54440
In triangle ABC, we have AC = BC = 7 and AB = 2. Suppose that D is a p  [#permalink]

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24 Mar 2019, 23:03
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Difficulty:

55% (hard)

Question Stats:

67% (04:10) correct 33% (02:07) wrong based on 14 sessions

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In triangle ABC, we have AC = BC = 7 and AB = 2. Suppose that D is a point on line AB such that B lies between A and D and CD = 8. What is BD ?

(A) 3

(B) $$2\sqrt{3}$$

(C) 4

(D) 5

(E) $$4\sqrt{2}$$

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Joined: 27 Sep 2018
Posts: 37
Re: In triangle ABC, we have AC = BC = 7 and AB = 2. Suppose that D is a p  [#permalink]

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24 Mar 2019, 23:29
Triangle CAB is isosceles triangle with base AB=2 and AC=BC=7

Dropping a perpendicular from C on AB at E will bisect AB I.e EB=1

Also triangle CEB will be right angled triangle, with hypotenuse CB=7, base EB=1, and perpendicular can be calculated using Pythagoras

Perpendicular= rt(CB^2-EB^2)=rt48

Also triangle CED is right angled triangle where perpendicular CE=rt48, hypotenuse, CD=8 and base ED=x

Using Pythagoras find ED
ED=rt(8^2-48)=rt16=4
BD=ED-EB=4-1=3

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Re: In triangle ABC, we have AC = BC = 7 and AB = 2. Suppose that D is a p   [#permalink] 24 Mar 2019, 23:29
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