Four Points in The Plane

We are given points A,B,C and D in the plane such that AD=13, whereas AB=BC=AC=CD=10. Compute the measure of \angle{ADB} in degrees.
Source: NCTM Mathematics Teacher

SOLUTION

C is the center of a circle of radius 10 passing through points A,B,D. The central \angle{BCA}=60^\circ because \triangle{ABC} is equilateral. \angle{ADB} is an inscribed angle that intercepts arc AB,
\angle{ADB}=\displaystyle\frac{60^\circ}{2}=30^\circ.

Answer: 30^\circ

Advertisements

About mvtrinh

Retired high school math teacher.
This entry was posted in Problem solving and tagged , , , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s