Given triangle ABC. Construct a circle (J) passing through A and having B as point of tangency, a circle (K) passing through B and having C as point of tangency. (J) intersects (K) at P . Prove that (PCA) has A as point of tangency.
#Please help me with my exercise
night umbra
blazing impBOT
Given triangle ABC. Construct a circle (J) passing through A and having B as poi...
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dusty pond
Given triangle ABC. Construct a circle (J) passing through A and having B as poi...
u have done it here..
like it intersects AB...
so yea thats all..or prob ur q is unclear
high ingot
Given triangle ABC. Construct a circle (J) passing through A and having B as poi...
This feels poorly translated.
night umbra
This feels poorly translated.
Given triangle ABC. Construct a circle (J) passing through A and having B as tangential point, a circle (K) passing through B and having C as tangential point. (J) intersects (K) at P . Prove that (PCA) has A as tangential point.
@high ingot Is this more clear?
high ingot
<@352737152154468352> Is this more clear?
More clear, yes, but there's no such thing as a "tangential point".
high ingot
What do you think the word "tangent" means?
rustic geode
"point of tangency" would be more correct here
teal agate
"Point at which this line is tangent to the curve"
night umbra
What do you think the word "tangent" means?
I think the only point that a line intersects a circle?
rustic geode
I think the only point that a line intersects a circle?
not necessarily intersecting.
what angle does a tangent line make with a circle?
high ingot
I think the only point that a line intersects a circle?
"Tangent" is an adjective describing a curve which intersects another curve at a single point where the derivatives of the two curves have the same value.
That is, the two curves have the same "immediate slope".
night umbra
what angle does a tangent line make with a circle?
i think an angle = 90° made with radius and tangent line
rustic geode
i think an angle = 90° made with radius and tangent line
yes
thats really what a "point of tangency is"
the point on the tangent line where it touches the circle
night umbra
@high ingot @teal agate @rustic geode Thank you for helping me understand the concept and the correct spelling of that
desert jungleBOT
@night umbra has given 1 rep to @rustic geode @high ingot @teal agate
high ingot
Given triangle ABC. Construct a circle (J) passing through A and having B as poi...
So what we would actually say is that (J) is tangent to AC at A, (K) is tangent to BC at C, and (PCA) is tangent to AB at A. If you don't talk about the curve the circle is tangent to, you're not giving any information, because there's infinitely many curves which are tangent to any other curve at any given point.
Or... something like that. It's not entirely clear from the way you said it which lines the circles are supposed to be tangent to.
night umbra
So what we would *actually* say is that `(J)` is tangent *to* `AC` *at* `A`, `(K...
i mean we need to prove that (PCA) is tangent to AB at A
we only have (J) is tangent to AC at A, (K) is tangent to BC at C and (J) intersects (K) at P
high ingot
Right. Because it can't be tangent to AC since it passes through both A and C, and it can't be tangent to BC at A.
Hmm. How many circles are there that pass through B and are tangent to AC at A?
night umbra
Hmm. How many circles are there that pass through B and are tangent to AC at A?
i think none
high ingot
i think none
...so (J) doesn't exist?
night umbra
...so (J) doesn't exist?
(K)
high ingot
No, I meant (J).
night umbra
No, I meant (J).
I think it passes through A and is tangent to BC at B
night umbra
Post the original question.
but it is not in English
high ingot
but it is not in English
Does it use the Latin alphabet?
night umbra
Does it use the Latin alphabet?
it is Vietnamese
high ingot
Give a translation after.
night umbra
Give a translation after.
Datis triangulo ABC. (J) transit per A, B ut JB sit perpendicularis ad BC in B, (K) transit per B, C, ut sit KC perpendicularis in AC in C. Proba quod CA contingens PCA in A
high ingot
Datis triangulo ABC. (J) transit per A, B ut JB sit perpendicularis ad BC in B, ...
A picture of the original question.
night umbra
A *picture* of the original question.
Ok
night umbra
A *picture* of the original question.
Do you the question in Vietnamese?
@high ingot
smoky crystal
Do you the question in Vietnamese?
just send a picture, we can translate accordingly
modest portalBOT
@night umbra