Homework Help: geometry

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

Answer this Question

Related Questions

Geometry - in circle p below the lengths of the parallel chords are 20,16, and ...
geometry - Two parallel chords lie on opposite sides of the centre of a circle ...
geometry - Two parallel chords lie on opposite sides of the centre of a circle ...
math - in circle p below the lengths of the parallel chords are 20,16, and 12. ...
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 ...
Math - Two chords intersect inside a circle. The lengths of the segment of one ...
Geometry - Suppose that line t is tangent to circle center O and radius OP at ...
geometry - Two chords intersect a circle. The shorter chord is divided into ...
Geometry - Prove that the tangents to a circle at the endpoints of a diameter ...

For Further Reading

First Name:
School Subject:
Answer: