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

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New post 14 Sep 2018, 00:54
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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
image036.jpg [ 2.86 KiB | Viewed 288 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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New post 14 Sep 2018, 01:11
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Bunuel wrote:
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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:
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

Answer: option B
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Geometry 7 Similar Triangle Latest.jpg
Geometry 7 Similar Triangle Latest.jpg [ 195.88 KiB | Viewed 229 times ]


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Re: If A and B are tangent to the circle with center O as shown in the fig &nbs [#permalink] 14 Sep 2018, 01:11
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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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