The diagram shows a semicircle of radius 1 inside an isosceles triangle. The diameter of the semicircle lies along the "base" of the triangle, and the angle of the triangle opposite the "base" is equal to . Each of the two equal sides of the triangle is tangent to the semicircle.
What is the area of the triangle?
Select one option, then click Submit.
\frac{1}{2} \tan 2\theta
\sin \theta \cos \theta
\sin \theta + \cos \theta
\frac{1}{2} \cos 2\theta
\frac{1}{\sin \theta \cos \theta}
Select an option, then submit.
Sign in or create an account to reveal answers, view the solution, and save your progress. Create a free account to unlock practice and keep track of your work.
Senior Mathematical Challenge 2018 (2018)
One puzzle per day. Cryptarithm, Magic Square, Summit. No sign-up required to play.
Play daily puzzle →Interactive problems and curated lessons—water pouring, magic squares, knight's tour, and more.
Browse library →See how you rank. Top solvers by problems solved correctly. Sign in to climb the ranks.
View leaderboard →Senior Mathematical Challenge 2018 (2018)