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If A and B are tangent to the circle with center O as shown in the fig

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Joined: 02 Sep 2009
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If A and B are tangent to the circle with center O as shown in the fig  [#permalink]

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14 Sep 2018, 01:54
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Difficulty:

35% (medium)

Question Stats:

60% (02:21) correct 40% (01:30) wrong based on 5 sessions

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If A and B are tangent to the circle with center O as shown in the figure above, and AD has a length of 5 and AC has a length of 13, what is the radius of the circle?

A. 25/12

B. 65/12

C. $$\sqrt{34}$$

D. $$\sqrt{41}$$

E. $$\sqrt{50}$$

Attachment:

image036.jpg [ 2.86 KiB | Viewed 371 times ]

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Re: If A and B are tangent to the circle with center O as shown in the fig  [#permalink]

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14 Sep 2018, 02:11
1
Bunuel wrote:

If A and B are tangent to the circle with center O as shown in the figure above, and AD has a length of 5 and AC has a length of 13, what is the radius of the circle?

A. 25/12

B. 65/12

C. $$\sqrt{34}$$

D. $$\sqrt{41}$$

E. $$\sqrt{50}$$

Attachment:
The attachment image036.jpg is no longer available

Triangle ADC is a right angle triangle with AC = 13 and AD = 5 i.e. CD = 12

Triangles ACD and OAD are similar triangle as per the property derived in attachment
hence,
AD / CD = OA / AC
OA = Radius = (5/12)*13 = 65/12

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Geometry 7 Similar Triangle Latest.jpg [ 195.88 KiB | Viewed 304 times ]

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Re: If A and B are tangent to the circle with center O as shown in the fig   [#permalink] 14 Sep 2018, 02:11
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