Angles in Circles: Triangle with Diameter Hypotenuse

over 1 year ago

In this video I go over a quick proof video on the topic of angles within circles. In this proof video, I show that the middle angle of a triangle drawn inside a circle in which the diameter of the circle forms the hypotenuse of the triangle is in fact a right angle, i.e. 90 degrees. To prove this I first draw the triangle and then split the triangle into two triangles by drawing a line from the origin of the circle to the middle point. This utilizes the fact that the we then have 3 lines, or sides of the two triangles, that equal in distance to the radius of the circle. This also means that we obtain two isosceles triangles with equal sides equal to the radius, thus each triangle contains two sides with the same angle. Using this fact, as well as the fact that the sum of angles inside a triangle equal to 180 degrees, and the sum of angles along a straight line are also equal to 180 degrees, we can then do some algebra to show that indeed the middle angle of the larger triangle, or summation of two angles in the two smaller triangles, is equal to 90 degrees, thus being a right angle. This run-on sentence that I just wrote is nonetheless a good explanation of the steps taken in the proof. This is a really interesting video to show how to play around with angles and triangles within circles, so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhul7FPjsP3smxcW_eQ

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/video-notes-angles-in-circles-triangle-with-diameter-hypotenuse