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14 Nov 2019, 00:42
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D
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:
72% (02:12) correct
28%
(02:21)
wrong
based on 106
sessions
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In the figure shown, O is the centre of the circle. What is the value of x+y+z?
A. 104
B. 112
C. 180
D. 188
E. 196
Attachment:
Geometry.JPG [ 9.92 KiB | Viewed 7533 times ]
14 Nov 2019, 01:01
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Let the radius of the circle = r
Note that, OA = OB = OC = r
--> triangle OAB & OBC are isosceles
--> ∠A = ∠B = x
In triangle OAB, ∠A + ∠B + 100 = 180
--> 2x + 100 = 180
--> 2x = 80
--> x = 40
Consider the straight line AT,
--> ∠B + y + 108 = 180 (straight angle)
--> x + y = 72
--> y = 72 - x = 72 - 40 = 32
In triangle OBC, ∠B = ∠C = y
--> ∠z + ∠y + ∠y = 180
--> ∠z = 180 - 64 = 116
So, x + y + z = 40 + 32 + 116 = 188
IMO Option D
Note that, OA = OB = OC = r
--> triangle OAB & OBC are isosceles
--> ∠A = ∠B = x
In triangle OAB, ∠A + ∠B + 100 = 180
--> 2x + 100 = 180
--> 2x = 80
--> x = 40
Consider the straight line AT,
--> ∠B + y + 108 = 180 (straight angle)
--> x + y = 72
--> y = 72 - x = 72 - 40 = 32
In triangle OBC, ∠B = ∠C = y
--> ∠z + ∠y + ∠y = 180
--> ∠z = 180 - 64 = 116
So, x + y + z = 40 + 32 + 116 = 188
IMO Option D
14 Nov 2019, 01:10
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In the figure shown, O is the centre of the circle. What is the value of x+y+z?
A. 104
B. 112
C. 180
D. 188
E. 196
From figure we have following:
AO = BO = radius of circle
Thus, x = angle(ABO)
Now x + x + 100 = 180 for triangle(ABO)
x = 40
Similarly,
BO = CO = radius of circle
y = angle(BCO)
Now, y + y + z = 180
Also at point B x + y + 108 = 180 (straight line)
y = 32
Hence 32 + y + z = 180
OR
x + y + z + 32 = 180 + x
x + y + z = 180 + 40 - 32 = 188
Answer D.
A. 104
B. 112
C. 180
D. 188
E. 196
From figure we have following:
AO = BO = radius of circle
Thus, x = angle(ABO)
Now x + x + 100 = 180 for triangle(ABO)
x = 40
Similarly,
BO = CO = radius of circle
y = angle(BCO)
Now, y + y + z = 180
Also at point B x + y + 108 = 180 (straight line)
y = 32
Hence 32 + y + z = 180
OR
x + y + z + 32 = 180 + x
x + y + z = 180 + 40 - 32 = 188
Answer D.
