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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
Joined: 02 Sep 2009
Posts: 58381
Two tangents to a circle are drawn from a point A. The points of conta  [#permalink]

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31 Mar 2019, 22:37
00:00

Difficulty:

35% (medium)

Question Stats:

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

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Two tangents to a circle are drawn from a point A. The points of contact B and C divide the circle into arcs with lengths in the ratio 2:3. What is the degree measure of angle BAC?

A. 24
B. 30
C. 36
D. 48
E. 60

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

Attachment:

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
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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