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Two tangents to a circle are drawn from a point A. The points of conta

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Math Expert
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Two tangents to a circle are drawn from a point A. The points of conta  [#permalink]

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New post 31 Mar 2019, 22:37
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

79% (02:10) correct 21% (02:38) wrong based on 34 sessions

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Joined: 24 Jun 2018
Posts: 35
Re: Two tangents to a circle are drawn from a point A. The points of conta  [#permalink]

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New post 08 Apr 2019, 05:06
2
Refer the below image.


Attachment:
Screenshot 2019-04-08 at 17.24.19.png
Screenshot 2019-04-08 at 17.24.19.png [ 40.29 KiB | Viewed 352 times ]


It has been given in the question minor arc BC/Major arc BC = 2/3

ie. the circle has been divided into two arcs in the ratio 2:3. A circle that is made of 360 degrees is divided in 2/3 ratio

Hence to calculate the measure of individual parts 2 and 3, we follow the conventional approach to calculate ratios

2x + 3x = 5x = 360 deg

x = 72 deg

From image it is clear that in the quadrilateral ABOC, angle BOC = 2x = 144 deg

Now in the quadrilateral, ABO = 90 deg and ACO = 90 deg {Since a tangent is always perpendicular to the center of circle at the point of contact}

And hence BOC + BAC= 180 deg
since BOC = 144

we get BAC = 36 deg
GMAT Club Bot
Re: Two tangents to a circle are drawn from a point A. The points of conta   [#permalink] 08 Apr 2019, 05:06
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Two tangents to a circle are drawn from a point A. The points of conta

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