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In the figure above, point O is the center of the circle and
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25 May 2020, 09:07
25 May 2020, 09:07
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56% (02:37) correct
43% (02:45) wrong based on 48 sessions
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In the figure above, point O is the center of the circle and OC = AC = AB. What is the value of x ?
(A) 40
(B) 36
(C) 34
(0) 32
(E) 30
Re: In the figure above, point O is the center of the circle and
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25 May 2020, 09:08
25 May 2020, 09:08
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In the figure above, point O is the center of the circle and
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25 May 2020, 09:49
25 May 2020, 09:49
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Carcass wrote:
In the figure above, point O is the center of the circle and OC = AC = AB. What is the value of x ?
(A) 40
(B) 36
(C) 34
(0) 32
(E) 30
Since OC = AC, ∆AOC is an isosceles triangle, which means ∠OAC is also x°
Since all 3 angles in ∆AOC must add to 180°, we can conclude that ∠OCA = (180-2x)°
Since angles on a LINE must add to 180°, we can conclude that ∠ACB = 2x°
Since AC = AB, ∆ACB is an isosceles triangle, which means ∠CBA is also 2x°
Finally, since OA and OB are radii of the same circle, we know that ∆OAB is an isosceles triangle, which means ∠OABis also 2x°
At this point, we can see that the 3 angles ∆OAB are x°, 2x° and 2x°
Since the angles in a triangle must add to 180°, we can write: x° + 2x° + 2x° = 180°
Simplify: 5x = 180
Solve: x = 36
Answer: B
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