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# If the lines shown in the picture touch the circle with center O only

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Math Expert
Joined: 02 Sep 2009
Posts: 52902
If the lines shown in the picture touch the circle with center O only  [#permalink]

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04 Sep 2018, 22:49
00:00

Difficulty:

35% (medium)

Question Stats:

76% (01:06) correct 24% (00:56) wrong based on 27 sessions

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If the lines shown in the picture touch the circle with center O only at points A and B, what is the area of the triangle ABC?

(1) Triangle ADC has area of 25.
(2) Triangle BDC has area of 25.

Attachment:

image008.gif [ 2.78 KiB | Viewed 277 times ]

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Re: If the lines shown in the picture touch the circle with center O only  [#permalink]

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05 Sep 2018, 04:17
Bunuel wrote:

If the lines shown in the picture touch the circle with center O only at points A and B, what is the area of the triangle ABC?

(1) Triangle ADC has area of 25.
(2) Triangle BDC has area of 25.

Attachment:
image008.gif

Question stem:- What is the area of the triangle ABC?

In the triangles, ADC and BDC:
a) AC=BC
b) Angle ACD=Angle BCD
c) CD is the common side

hence $$\triangle{ADC}$$ and $$\triangle{BDC}$$ are congruent(S-A-S).

Therefore are of both the triangles are equal. or, Area of triangle ABC=2* Area of triangle ADC=2*Area of triangle BDC

St1:-Triangle ADC has area of 25.
Sufficient.

St2:-Triangle BDC has area of 25.
Sufficient.

Ans. (D)
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Re: If the lines shown in the picture touch the circle with center O only   [#permalink] 05 Sep 2018, 04:17
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