orahmokwena903
Answered

Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

In the diagram A, B, and C are the points on the circle. Use the diagram to prove the theorem which states that:
if O is the center of the circle then AÔB = 2Ĉ.
​

In The Diagram A B And C Are The Points On The Circle Use The Diagram To Prove The Theorem Which States Thatif O Is The Center Of The Circle Then AÔB 2Ĉ class=

Sagot :

sqdancefan

9514 1404 393

Explanation:

Here's one way to go at it.

Draw segments AB and CO. Define angles as follows. (The triangles with sides that are radii are all isosceles, so their base angles are congruent.)

  x = angle OAB = angle OBA

  y = angle OAC = angle OCA

  z = angle OBC = angle OCB

Consider the angles at each of the points A, B, C.

At A, we have ...

  angle CAB = x + y

At B, we have ...

  angle CBA = x + z

At C, we have ...

  angle ACB = y + z

The sum of the angles of triangle ABC is 180°, as is the sum of angles in triangle ABO. This gives ...

  x + x + ∠AOB = (x+y) +(x+z) +(y+z)

  ∠AOB = 2(y+z) = 2∠ACB

This shows ∠AOB = 2×∠C, as required.

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.