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15 Nov 2021, 06:45
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D
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Difficulty:
95%
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Question Stats:
14% (02:15) correct
86%
(03:14)
wrong
based on 21
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In the circle above the length of the minor arc AB is \(10\pi\) and the length of the minor arc CD is \(3\pi\). What is the measure of angle F, if the radius of the circle is 18?
(A) 20
(B) 25
(C) 30
(D) 35
(E) 40
Attachment:
1.jpg [ 7.13 KiB | Viewed 2270 times ]
15 Nov 2021, 07:44
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The angle subtend by arc AB at the centre is 100 and the angle subtend by arc CD at the center is 30. Therefore angle ACB is 50 and angle CBD is 15 respectively.
This makes BCF = 130 and hence angle CFB is 35.
IMO D
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This makes BCF = 130 and hence angle CFB is 35.
IMO D
Posted from my mobile device
28 Nov 2021, 09:13
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Bunuel
Please refer to the attached fig.
Attachment:
Finding angle F.png [ 79.54 KiB | Viewed 1876 times ]
This question makes use of the central angle theorem :
The Central Angle Theorem states that the central angle from two chosen points C and D on the circle is always twice the inscribed angle from those two points. The inscribed angle can be defined by any point along the outer arc CD and the two points C and D
Calculating central angle \(y\) for minor arc CD\(=\frac{360}{2 \pi 18} = \frac{y}{3 \pi}\), \(y= 30\) refer diagram 1 in attached fig.
Calculating central angle \(x \) for minor arc AB \(= \frac{360}{2 \pi 18} = \frac{x}{10 \pi}\), \(x= 100\) refer diagram 2 in attached fig.
Hence in \(\Delta\) BCF we have \(\angle B =15 \) and \(\angle C = 130\)
Hence\( \angle F \) = \(180- 145 = 35\)
Ans D
Hope it's clear.
