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In the figure above, is the diameter of a circle. Is the area of ΔABD  [#permalink]

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In the figure above AC, is the diameter of a circle. Is the area of ΔABD equal to the area of ΔBCD ?

(2) BD= 5

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In the figure above, is the diameter of a circle. Is the area of ΔABD  [#permalink]

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Hello KanishkM rinkumaa4

Official Explanation

This is a Yes/No Data Sufficiency question. However, there is information in the question stem that should be considered, so use the Pieces of the Puzzle approach to assess the question. The question asks whether the area of triangle ABD is equal to the area of triangle BCD. Since the two triangles share a common height, BD, their areas will be equal only if their bases, AD and DC, are the same length. Therefore, in order to answer the question, the statements must provide information sufficient to determine whether AD = DC. The task of a Yes/No Data Sufficiency question is to determine whether the information in the statements produces a consistent “Yes” or “No” answer to the question. Evaluate the statements one at a time.

Evaluate Statement (1). The length of AD is 2. However, Statement (1) does not provide the length of DC, so it is insufficient to determine whether AD = DC. Write down BCE.

Now, evaluate Statement (2). The length of BD is 5. However, Statement (2) does not provide the lengths of AD and DC, so it is insufficient to determine whether AD = DC. Eliminate (B).

Now, evaluate both statements together. Recognize that triangles ABD and BCD together form a larger triangle, triangle ABC. The Inscribed Angle Theorem dictates that angle ABC must be 90°, so triangle ABC is a right triangle, and $$(AB)^2 + (BC)^2 = (AC)^2$$. From Statement (1), AD = 2. Therefore, AC = DC + 2. Substitute this value of AC into the equation above, so that $$(AB)^2 + (BC)^2 = (DC + 2)^2$$. If the values of $$(AB)^2$$ and $$(BC)^2$$ can be determined, then the length of DC can be determined. Determine the value of $$(AB)^2$$. If AD = 2 and BD = 5, then $$2^2 + 5^2 = (AB)^2$$. Simplify the equation, so that $$(AB)^2 = 29$$. Substitute this value of $$(AB)^2$$ into the equation above, so that $$29 + (BC)^2 = (DC + 2)^2$$. Now, determine the value of $$(BC)^2$$. If BD = 5, then $$(DC)^2 + 5^2 = (BC)^2$$. Simplify the equation, so that $$(BC)^2 = (DC)^2 + 25$$. Substitute this value of $$(BC)^2$$ into the equation above, so that $$29 + (DC)^2 + 25 = (DC + 2)^2$$. Simplify the equation, so that $$(DC)^2 + 54 = (DC)^2 + 4(DC) + 4$$. Combine like terms, so that 50 = 4(DC). Divide both sides of the equation by 4, so that (DC) = 12.5. Since (DC) ≠ (AD), the areas of triangles ABD and BCD are not the same, and the answer is “No.”

Together, both statements are sufficient to answer the question, so eliminate (E). The correct answer is (C).

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Re: In the figure above, is the diameter of a circle. Is the area of ΔABD  [#permalink]

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Attachment:
1111.jpg

In the figure above,is the diameter of a circle. Is the area of ΔABD equal to the area of ΔBCD ?

(2) BD= 5

AC is the diameter, right??
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Director  G
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In the figure above, is the diameter of a circle. Is the area of ΔABD  [#permalink]

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Attachment:
1111.jpg

In the figure above AC, is the diameter of a circle. Is the area of ΔABD equal to the area of ΔBCD ?

(2) BD= 5

IMO C

Since AC is the diameter < ABC = 90, angle subtended in a semi circle is 90

DB = AD= DC, they all are radius, <DAB = <ABD = 45, So actually by SAS, both triangles can be equal

Area of triangle ABD = Area of triangle BCD

The ratio will be equal to the square of the corresponding sides to the corresponding angles, said that

Area of triangle ABD / Area of triangle BCD = (AD/DC)^2
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Originally posted by KanishkM on 10 Feb 2019, 04:23.
Last edited by KanishkM on 16 Feb 2019, 09:34, edited 1 time in total.
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Re: In the figure above, is the diameter of a circle. Is the area of ΔABD  [#permalink]

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KanishkM wrote:
Attachment:
1111.jpg

In the figure above AC, is the diameter of a circle. Is the area of ΔABD equal to the area of ΔBCD ?

(2) BD= 5

IMO D

Since AC is the diameter < ABC = 90, angle subtended in a semi circle is 90

DB = AD(radius), <DAB = <ABD = 45 and same goes for BD = DC(radius), < DBC = <BCD = 45

From 1) AD = 2, BD = 2
area of ΔABD is equal to the area of ΔBCD

From 2) BD = 5
area of ΔABD is equal to the area of ΔBCD

I DONT THINK SO

No where D is the center given and we cant infer it also
Director  G
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Re: In the figure above, is the diameter of a circle. Is the area of ΔABD  [#permalink]

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rinkumaa4 wrote:

I DONT THINK SO

No where D is the center given and we cant infer it also

rinkumaa4

I agree with your thoughts ,I didn't get this one.

Answer is some other option Can you please share your thoughts on this.

TIA
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Re: In the figure above, is the diameter of a circle. Is the area of ΔABD  [#permalink]

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KanishkM wrote:
rinkumaa4 wrote:

I DONT THINK SO

No where D is the center given and we cant infer it also

rinkumaa4

I agree with your thoughts ,I didn't get this one.

Answer is some other option Can you please share your thoughts on this.

TIA

Ok,

I think it is DS question and for me, we cant infer anything from the image.

So each 1 and 2 are insuff.

Both 1+2.

Say D is not the center point and neither the angle ADB or CDB is a right angle.
As AD=2 and BD=5
no away the area will be equal.

so IMO C.
Director  G
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In the figure above, is the diameter of a circle. Is the area of ΔABD  [#permalink]

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rinkumaa4 wrote:
KanishkM wrote:
rinkumaa4 wrote:

I DONT THINK SO

No where D is the center given and we cant infer it also

rinkumaa4

I agree with your thoughts ,I didn't get this one.

Answer is some other option Can you please share your thoughts on this.

TIA

Ok,

I think it is DS question and for me, we cant infer anything from the image.

So each 1 and 2 are insuff.

Both 1+2.

Say D is not the center point and neither the angle ADB or CDB is a right angle.
As AD=2 and BD=5
no away the area will be equal.

so IMO C.

rinkumaa4

I got it, I can agree with your reasoning.

My second guess could have been an E

Thank you
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Re: In the figure above, is the diameter of a circle. Is the area of ΔABD  [#permalink]

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KanishkM

Yes may be. But can you explain if D is not the center of the semi-circle, then How can the two tri-angle become equal?

I did not get that point.
Please Explain and clear my doubt.

Regards
Abhisek
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Re: In the figure above, is the diameter of a circle. Is the area of ΔABD  [#permalink]

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rinkumaa4 wrote:
KanishkM

Yes may be. But can you explain if D is not the center of the semi-circle, then How can the two tri-angle become equal?

I did not get that point.
Please Explain and clear my doubt.

Regards
Abhisek

I guess you meant, when D is the center ?

If yes, then actually we can say

Since AC is the diameter < ABC = 90, angle subtended in a semi circle is 90

DB = AD= DC, they all are radius, <DAB = <ABD = 45, So actually by SAS, both triangles can be equal

Area of triangle ABD = Area of triangle BCD

The ratio will be equal to the square of the corresponding sides to the corresponding angles

said that

Area of triangle ABD / Area of triangle BCD = (AD/DC)^2

IMO, It will be equal

I think i got the answer.

C
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Re: In the figure above, is the diameter of a circle. Is the area of ΔABD  [#permalink]

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Hi Kanishk,

Here we have to give answer yes or no.

If you use both choice you can certainly say the area is not equal .

So our answer is No

Hence otion C .

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Giving Kudos is the best way to encourage and appreciate people Re: In the figure above, is the diameter of a circle. Is the area of ΔABD   [#permalink] 16 Feb 2019, 09:37
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