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13 Jun 2022, 04:15
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
81% (01:57) correct
19%
(02:08)
wrong
based on 21
sessions
History
Date
Time
Result
Not Attempted Yet
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
A. 24
B. 30
C. 36
D. 48
E. 60
15 Jun 2022, 11:52
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Consider the above image.
- Here, the length of the minor arc BC: the length of the major arc BC = 2:3
- This means the ratio of the obtuse ∠BOC (the smaller one) to the reflex ∠BOC (the larger one) = 2 : 3.
- So the obtuse ∠BOC =\( \frac{2}{5 } × 360 = 144\)
- We know ∠OBA = ∠OCA = 90 (Tangent property)
Thus, ∠BAC = 360 - 90 - 90 - 144 = 36
The answer is D.
Note: I have drawn OA here but that is not needed.
