Abbreviate Cricle Geometry prooofs (1 Viewer)

[Dragonmaster262]

Some circle geometry proofs are too long and waste too much time. Does anyone have shortened versions of the below proofs?

1) The square of the length of the tangent from an external point is equal to the product of the intercepts of the secant passing through this point.

2) The angle between the tangent ans the chord through the point of contact is equal to the angle in the alternate segment.

 

[Aquawhite]

I have rarely ever been asked to proove these properties of a circle. I am always to know them and apply them in individual situations.

Sorry, I can't help. I can imagine that the proof would be quite long and tedious.

 

[lychnobity]

Some circle geometry proofs are too long and waste too much time. Does anyone have shortened versions of the below proofs?

1) The square of the length of the tangent from an external point is equal to the product of the intercepts of the secant passing through this point.

Tangent's squared length = secant's product of intercepts, from same ext. point

or

Tangent's squared length = secant's intercepts' product from same ext. point

2) The angle between the tangent ans the chord through the point of contact is equal to the angle in the alternate segment.

(not recommended) alt segment theorem

or

angle between tangent & chord to point of contact = angle in alt segment

 

[Timothy.Siu]

i just write 2 or 3 words like what lynch said nto to do,
angle in alt. segment,.

 

[shady145]

Tangent's squared length = secant's product of intercepts, from same ext. point



(not recommended) alt segment theorem

or

angle between tangent & chord to point of contact = angle in alt segment

ahhhhhhhhhhhh my teacher tells me to use that one... if it means anything she marks HSC papers =S

 

[EvoRevolution]

I was told that you do not have to write the whole wording, just name the Theorem e.g tangent-radius theorem, i think the HSC markers only require you to identify the theorem.

Not 100% sure, but as long as u try to explain to them what you have done you should be fine

 

[astroe]

i just write 2 or 3 words like what lynch said nto to do,
angle in alt. segment,.

I agree with this statement.

 

[cutemouse]

Wasn't there something about this that they DIDN'T allow abbreviations for one year?

 

[Dragonmaster262]

Tangent's squared length = secant's product of intercepts, from same ext. point

or

Tangent's squared length = secant's intercepts' product from same ext. point



(not recommended) alt segment theorem

or

angle between tangent & chord to point of contact = angle in alt segment

Why do you not recommend this?

 

[ninetypercent]

externally, you can abbreviate.. as long as the reasoning is understandable

internally, it depends on your school. At my school, you are required to write the FULL SENTENCE OUT. Otherwise, you lose all the marks.