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Re: If O is the center of the circle with diameter AB and T is a tangency [#permalink]
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fskilnik wrote:
GMATH practice exercise (Quant Class 7)



If O is the center of the circle with diameter AB and T is a tangency point, what is the value of x?

(A) 10
(B) 15
(C) 18
(D) 20
(E) 22.5


A radius drawn to a tangent point yields a RIGHT ANGLE:

In the figure above:
Radius OT forms a right angle at tangent point T.
OA and OT are radii and thus are equal.
Since OA=OT, opposite angles OAT and ATO are equal.

We can PLUG IN THE ANSWERS, which represent the value of x.
From left to right, option D yields the following 3 triangles:

In this case, the resulting angle sum for the green triangle is TOO BIG:
20+80+90 = 190.
Eliminate D.

From left to right, option B yields the following 3 triangles:

In this case, the resulting angle sum for the green triangle is TOO SMALL:
15+60+90 = 165.
Eliminate B.

Since D yields a sum that is TOO BIG, while B yields a sum that is TOO SMALL, the correct answer must be BETWEEN B AND D.

.
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Re: If O is the center of the circle with diameter AB and T is a tangency [#permalink]
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