2010 AMC 10B Problem 6

Attempt Problem 6 of the 2010 AMC 10B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2010 AMC 10B solutions, or check the answer key.

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6.

A circle is centered at O,O, AB\overline{AB} is a diameter and CC is a point on the circle with COB=50.\angle COB = 50^\circ. What is the degree measure of CAB?\angle CAB?

2020

2525

4545

5050

6565

Answer: B
Concepts:circleisosceles triangleangle chasing
Difficulty rating: 960
Solution:

Consider the following diagram:

We have that AOC=18050=130. \angle AOC = 180^{\circ} - 50^{\circ} = 130^{\circ}.

Since AOC\triangle AOC is isosceles, we have that CAO=1801302=25. \angle CAO = \dfrac{180^{\circ} - 130^{\circ}}{2} = 25^{\circ}.

Since CAB=CAO,\angle CAB = \angle CAO, we have that CAB=25.\angle CAB = 25^{\circ}.

Thus, B is the correct answer.

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