points A, B, C, D, E and F lie on the circumference of a circle.
Prove that angle ABC + angle CDE + angle EFA = 360 degrees
Draw a circle with all the points on the circumference and the centre labelled. Also, connect each points to the centre.
There are 6 different isosceles triangles with different base angles, call them angle 1, angle 2, angle 3, angle 4, angle 5, angle 6.
For each triangle, the remaining angle is 180-2(base angle)
Ex: For triangle OBC, remaining angle is 180-2(angle 1)
The sum of all remaining angles is 360.
180-2(angle 1)+180-2(angle 2)+...+180-2(angle 6)=360
Simplify this, angle 1 + angle 2 +...+ angle 6=360
angle ABC = angle 2 + angle 1
angle CDE = angle 6 + angle 5
angle EFA = angle 3 + angle 4
...
Hello, the undertaker!
Points lie on the circumference of a circle.
Prove that: .Code:A * o * * o o * * o o * F o o B o o *o o* *o o* *o o* o o E o o C * o o * * o o * * o * D
An inscribed angle is measured by one-half its intercepted arc.
Add [1], [2] and [3]:
. . . . . . . . . . . . .
. . . . . . . . . . . . .