Last visit was: 19 Jul 2024, 05:19 It is currently 19 Jul 2024, 05:19
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# If O is the center of the circle with diameter AB and T is a tangency

SORT BY:
Tags:
Show Tags
Hide Tags
Tutor
Joined: 12 Oct 2010
Status:GMATH founder
Posts: 891
Own Kudos [?]: 1416 [20]
Given Kudos: 56
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30834 [5]
Given Kudos: 799
General Discussion
Tutor
Joined: 12 Oct 2010
Status:GMATH founder
Posts: 891
Own Kudos [?]: 1416 [0]
Given Kudos: 56
Tutor
Joined: 04 Aug 2010
Posts: 1325
Own Kudos [?]: 3229 [0]
Given Kudos: 9
Schools:Dartmouth College
Re: If O is the center of the circle with diameter AB and T is a tangency [#permalink]
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.

.
Re: If O is the center of the circle with diameter AB and T is a tangency [#permalink]
Moderator:
Math Expert
94411 posts