Thread: Geometry of a Circle

Please help me solve these 3 problems relating to geometry of a circle.

1) ABCDEF is a hexagon inscribed in a circle. What is x + y + z?


2) In this figure, find the value of angle ABC + angle ADC and figure out if ABCD a cyclic quadrilateral. Therefore, find angle BDC


3a) In this figure, AOB is the diameter. Prove that points OAMP are concylic.
3b) Find two angles equal to angle OPA.


Thanks for any help.

Hello, BG5965!

1) is a hexagon inscribed in a circle. .What is ?

An inscribed angle is measured by one-half its intercepted arc.


We have: .


Add: .

. . . .

. . . .

Hello again, BG5965!

I have 3(b) . . .

3a) In this figure, is the diameter.
Prove that points OAMP are concylic.

3b) Find two angles equal to

I assume that is the center of the circle.

. . . both are radii.
Hence, is isosceles.
. . Therefore: .

. . . It is inscribed in a semicircle.
Right triangles and share angle
Then: .

. . Therefore: .