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# How far is point C from point B, which touches the circle as shown in

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
How far is point C from point B, which touches the circle as shown in  [#permalink]

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30 Aug 2018, 04:59
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Difficulty:

15% (low)

Question Stats:

83% (01:03) correct 18% (01:29) wrong based on 45 sessions

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How far is point C from point B, which touches the circle as shown in the figure?

(1) The radius of the circle is 5 units.
(2) Point C is 10 units away from the center of the circle.

Attachment:

image001 (1).gif [ 2.03 KiB | Viewed 613 times ]

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Re: How far is point C from point B, which touches the circle as shown in  [#permalink]

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30 Aug 2018, 05:08
Bunuel wrote:

How far is point C from point B, which touches the circle as shown in the figure?

(1) The radius of the circle is 5 units.
(2) Point C is 10 units away from the center of the circle.

Attachment:
image001 (1).gif

Let's join C with centre of circle and connect centre of circle with point of tangency.

Now OCA and OCB are right triangles with right angles at A and B

To find the length of CB we need other two sides of the triangle i.e.
1) OB (Radius of circle) and
2) OC (Distance between centre of circle and point C)

Question: BC = ?

Second requirement not satisfied hence

NOT SUFFICIENT

Statement 2: Point C is 10 units away from the center of the circle. i.e. OC = 10

Second requirement satisfied but radius is unknown hence

NOT SUFFICIENT

Combining the two statements

We have OB = 5 and OC = 10 hence

SUFFICIENT

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Re: How far is point C from point B, which touches the circle as shown in  [#permalink]

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30 Aug 2018, 09:07
Bunuel wrote:

How far is point C from point B, which touches the circle as shown in the figure?

(1) The radius of the circle is 5 units.
(2) Point C is 10 units away from the center of the circle.

Both statements are alone insufficient.

Combined, we have OBC is a right angled triangle with OB=5 , OC=10. (Refer enclosed diagram)
BC can be calculated using Pythagoras principle.
Sufficient.

Ans. (C)
Attachments

Tangent.JPG [ 27.01 KiB | Viewed 481 times ]

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How far is point C from point B, which touches the circle as shown in  [#permalink]

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30 Aug 2018, 13:13
Bunuel wrote:

How far is point C from point B, which touches the circle as shown in the figure?

(1) The radius of the circle is 5 units.
(2) Point C is 10 units away from the center of the circle.

Attachment:
The attachment image001 (1).gif is no longer available

Our solution is almost Algebra-free, as shown in the image below.

Important: Take your time to understand our GEOMETRIC BIFURCATIONS and, if necessary, please feel free to ask me about any detail related to it!

This solution follows the notations and rationale taught in the GMATH method.
Attachments

30Ago18_12z.gif [ 44.8 KiB | Viewed 417 times ]

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How far is point C from point B, which touches the circle as shown in   [#permalink] 30 Aug 2018, 13:13
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