Posted by **maya** on Monday, February 7, 2011 at 6:42pm.

given: chord AB is parallel to chord CD

prove if two chords of a circle are parallel, the two arcs between the chords are congruent.

Prove: arc AC is congruent to arc BD

- geometry -
**MathMate**, Monday, February 7, 2011 at 7:40pm
Draw a figure by hand and insert all the points, lines as angles as directed below in order to follow the proof.

Insert the centre of the circle and call it O, the radius of the circle is r.

Draw another line parallel to AB and CD through O and call it EF, where E is between A and C, F is between B and D.

Consider isosceles triangle ABO where AO=BO=r:

α=∠OAB=∠OBA (isosceles triangle)

Now consider parallel lines AB and EOF.

∠AOE=∠BAO (alternate angles)

∠BAO=∠ABO (isosceles triangle)

∠ABO=∠BOF (alternate angles)

Therefore

∠EOA=∠FOB

Similarly,

∠EOC=∠FOD

Thus

∠AOC=∠BOD

Length of arc AEC=r*∠AOC

Length of arc BFD=r*∠BOD

Therefore arc AEC = arc BFD

- geometry -
**Anonymous**, Wednesday, February 12, 2014 at 4:03pm
A circle has a diameter of 20 inches and a central angle AOB that measures 160°. What is the length of the intercepted arc AB? Use 3.14 for pi and round your answer to the nearest tenth

## Answer this Question

## Related Questions

- Geometry - in circle p below the lengths of the parallel chords are 20,16, and ...
- math - in circle p below the lengths of the parallel chords are 20,16, and 12. ...
- Geometry - Suppose that line t is tangent to circle center O and radius OP at ...
- geometry - there exists a circle with chords. the chords are congruent. their ...
- Geometry - The question is to find the measure of arc PQ in Circle A. The point ...
- circle - two parallel chords of length 30 cm and 16 cm are draw on the opposite ...
- circle - two parallel chords of length 30 cm and 16 cm are draw on the opposite ...
- Geometry - Two points are chosen uniformly at random on the unit circle and ...
- Circle Geometry - chords in a circle - Let PQ, RS , and TU be parallel chords of...
- Geometry - Two parallel chords lies on opposite sides of the centre of a circle ...