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04 Jun 2018, 09:00
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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:
35%
(medium)
Question Stats:
68% (01:32) correct
32%
(01:55)
wrong
based on 93
sessions
History
Date
Time
Result
Not Attempted Yet
What is the measure of angle ACB in the circle above with center O?
(1) The radius of the circle is 5.
(2) The length of the arc AB is 10.
Attachment:
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04 Jun 2018, 09:21
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Bunuel
Stat 1) ==> Not sufficient
stat2) ==> Not sufficient
Both ==> Length of arc AB= 10, from the formula for finding length of arc we have length arc AB = \(angle/360\)*2*pi*r
we can cal angle AOB,
Now in triangle OCB, we can find angle COB, which is Angle AOB - 180
finally, since triangle OCB is isosceles and we know angle COB from above ,we can easily find other two angle as they are equal.
so angle ACB equals angle ACB which is what we want ,,, hence suff
04 Jun 2018, 22:49
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Solution
Given:
- • The center of the circle is at O
To find:
- • The measure of the angle ACB
Approach and Working:
Given that, O is the center of the circle and C is a point on the circumference, we can say
- • Angle AOB = 2 * angle ACB
Therefore, if we know the value of the angle AOB, we can easily determine the value of the angle ACB
Analysing Statement 1
- • As per the information given in statement 1, the radius of the circle is 5
- o We can say, OA = OB = 5
o But we don’t know the length of the arc AB
o Therefore, we cannot find out the angle between OA and OB
Hence, statement 1 is not sufficient
Analysing Statement 2
- • As per the information given in statement 2, the length of the arc AB is 10
- o But, considering this statement only, we can’t find the angle between OA and OB, as we don’t know the length of the radius
Hence, statement 2 is not sufficient
Combining Both Statements
Combining the information from both the statements, we can say
- • OA = OB = 5 and length of arc AB = 10
• Using these information, we can easily find out the angle AOB
Therefore, we can find the angle ACB by combining the statements 1 and 2
Hence, the correct answer is option C.
Answer: C
