establishing a proof for angle formed in a circle by intercepting chords

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establishing a proof for angle formed in a circle by intercepting chords

Mathematics
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Following.
summoning the math gods and goddesses of OS
|dw:1437335161096:dw|

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I'm pretty certain you can look up the proofs online
what is the statement which we have to demonstrate?
|dw:1437335345728:dw|
vertical angles are congruent each other: |dw:1437335987601:dw|
correct
suppose we are given not the magnitudes of the chords but the angles of a and b how do we approach this?
to figure out x or F
is F the intersection point? right?
correct
I'm sorry I don't know
I think that we have to know at least one distance
for example the subsequent drawings have the same angles x |dw:1437337081389:dw|
so the position of point F is not determined uniquely
can we establish that \(\large \frac{\bar {ED}}{\bar {GH}} = \frac{\bar {AF}}{\bar {FE}}\) and \(\bar {EF} \times \bar {FG} = \bar{DF} \times \bar {FH}\) then we can use some trig identities perhaps

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