2: R.A.T. & Semi Circle


You might have seen in your school text book  that all right angled triangles inside a semi circle has to be a right angled triangle if its base is the diameter i.e. its hypotenuse is the diameter, d, as shown below. Now with your knowledge from Lesson 1, you can immediately write down the two other sides as dCos x and dSin x or if you know the other angle y, the sides will be dCos y and dSin y. Look below. 
Now, as usual, we must learn to look at the same thing from many different directions. This strengthens our geometrical vision and helps us in solving many problems easily. So, look at the diagram below. It should be very easy for you now to tell the sides. 
We have shown two more right angled triangles by turning the circle around. Become familiar with them. 
The diagram below shows many triangles drawn inside a circle each having its hypotenuse on the diameter and thus all of them are right angled triangles.

​Note that if the hypotenuse IS NOT the diameter, then triangles drawn inside a circle WILL NOT BE right angled triangles. 

Go to Geometry Lesson 3