### Tangent? Huh... what does that mean?

The tangent to a circle is a line that touches the circle at exactly one point. That point is known as the point of contact. GRE problem involving tangent almost always requires knowledge of this very important property:

The radius of the circle which joins the center of the circle to the point of contact (the tangent) is always perpendicular to the tangent.

In the figure above, line is a tangent to the circle with center at point of contact . Segment is a radius of the circle which is perpendicular to the tangent.

Example:

The above figure shows circle with center and a line that is tangent to circle at point . If point lies on line such that and radius of circle is , what is the area of the shaded region?

A)

B)

C)

D)

E)

Solution:

From the figure we know that the shaded region represents . To determine its area, we need to apply some special properties of the circle and the tangent. First lets organize the information provided:

Step 1: The problem states that line is tangent to circle at point . Further we also know that point lies on line .

Therefore . In addition we know that is a radius of the circle since is the center and is a point on the circumference of the circle. Since we know that radius of circle is, it follows that . We can redraw the figure based on this information:

Step 2: From the figure we know that is a right triangle with base and height . This is enough to calculate the area:

**B is the correct answer.**

## 6 comments:

A great blog with good information.

GTOEFL Exam Prep for International Students|GRE Prep Courses for International StudentsSomeone essentially lend a hand to make severely posts I would state. That is the very first time I frequented your website page and thus far? I surprised with the analysis you made to create this particular submit incredible. Fantastic job!

Office Interior Designers in Coimbatore

Office Interior Designers in Bangalore

Office Interior Designers in Hyderabad

I have definitely picked up anything new from right here. I did however expertise a few technical points using this site, since I experienced to reload the web site a lot of times previous to I could get it to load correctly.

Oracle Apps Training in Chennai

Android Training in Chennai

Informatica Training in Chennai

Excellent and very cool idea and the subject at the top of magnificence and I am happy to this post..Interesting post! Thanks for writing it. What's wrong with this kind of post exactly? It follows your previous guideline for post length as well as clarity..

Housekeeping services in Chennai

House cleaning service in Chennai

I do trust all of the concepts you’ve presented on your post. They’re really convincing and will definitely work. Still, the posts are too brief for newbies. May you please extend them a little from subsequent time?Also, I’ve shared your website in my social networks.

Pest Control in Chennai

Security Services in Chennai

Manpower services in Chennai

This site is very useful for this blog. thanks for giving information!!!!!!!!!!!!!!!!!

Cloud Computing Training in Chennai

## Post a Comment