Help with Circle Geometry? (1 Viewer)

[conjurring]

Hello,

Currently doing some circle geometry questions & having a bit of trouble. If you could help solve and provide an explanation for these questions, it'd be greatly appreciated.

1. AB and CD are two perpendicular chords of a circle, centre O. Prove that angle BOC + angle AOD = 180º.
2. Chord AC of circle, centre O, is equal to radius OA. Another chord CB is parallel to radius AO. Prove that CO is perpendicular to AB.

Thank you

 

[ProdigyInspired]

There's not really enough information on the first question, i.e. whether they intersect or not.

Are there any diagrams?

 

[ProdigyInspired]

For Q2, if you draw the diagram, you should be able to create a rhombus of sorts.

 

[conjurring]

There's not really enough information on the first question, i.e. whether they intersect or not.

Are there any diagrams?

Unfortunately there aren't diagrams included - but I have these diagrams drawn.

1)

2)

 

[conjurring]

1. 1. let < AOC = 2x
<ABC = x (angle at centre is twice angle at circumference)
let <DCB = y
< DOB = 2y (similarly)
Let E be the intersection of AB and CD
in triangle BCE,
< DCB + < ABC = 90 (< sum of triangle)
x + y = 90
< AOC + <DOB = 2x +2y
= 2 x 90
= 180
therefore, <BCO + < AOD = 180 ( angles in revolution)

Thank you Much appreciated.

 

[dan964]

Your diagram for 2 needs fixing as CO and AB do not intersect which is required for your question.