Okay, here's a problem made with fewer circles, tangents, secants, etc. See graphic

Geo Problem

Points \(A,B,C\) lie on a circle. A tangent is drawn through point \(A\). Secants are drawn through points \((A,B)\) and points \((B,C)\). The two secants intersect at point \(D\). Prove that these two inscribed angles are equal \(\angle DAC=\angle ABC\)

Here's a problem made to order for you, it has "circles, tangents, secants and inscribed angles" See graphic.

I Want A Problem

Two circles \(1\) and \(2\) are tangent at point \(A\). Points \((P, R)\) are on circle \(1\). A secant is drawn through points \((P,R)\), and tangents are drawn through point \(P\) and \(R\). These tangents intersect circle \(2\) at points \(Q\) and \(S\). Another secant is drawn through points \((Q,S)\), which intersects the other secant at point \(B\). Two more secants are drawn through points \((Q,A)\) and points \((S,A)\). Prove that the line drawn through points \((A,B)\) bisects the angle between those two secants. That is, prove that the inscribed angles the two secants through \((Q,A)\) and \((S,A)\) make with the line through \((A,B)\) are equal.

Maybe I should come up with another problem with half as many things, you know, a problem about a circle, a tangent, a secant, and an inscribed angle. It's not easy coming up with a problem with multiples of each.

How about if you posted a solution for me to another one of my geometry problems? This one

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

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TopNewestOkay, here's a problem made with fewer circles, tangents, secants, etc. See graphic

Geo Problem

Points \(A,B,C\) lie on a circle. A tangent is drawn through point \(A\). Secants are drawn through points \((A,B)\) and points \((B,C)\). The two secants intersect at point \(D\). Prove that these two inscribed angles are equal \(\angle DAC=\angle ABC\)

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Here's a problem made to order for you, it has "circles, tangents, secants and inscribed angles" See graphic.

I Want A Problem

Two circles \(1\) and \(2\) are tangent at point \(A\). Points \((P, R)\) are on circle \(1\). A secant is drawn through points \((P,R)\), and tangents are drawn through point \(P\) and \(R\). These tangents intersect circle \(2\) at points \(Q\) and \(S\). Another secant is drawn through points \((Q,S)\), which intersects the other secant at point \(B\). Two more secants are drawn through points \((Q,A)\) and points \((S,A)\). Prove that the line drawn through points \((A,B)\) bisects the angle between those two secants. That is, prove that the inscribed angles the two secants through \((Q,A)\) and \((S,A)\) make with the line through \((A,B)\) are equal.

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Michael, I hope you haven't given him more than he can handle ;)

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Maybe I should come up with another problem with half as many things, you know, a problem about a circle, a tangent, a secant, and an inscribed angle. It's not easy coming up with a problem with multiples of each.

How about if you posted a solution for me to another one of my geometry problems? This one

You can guess but can you prove it?

Everybody's "solving" this one, but nobody has actually put up a full proof.

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Check out the problems in Circles - Problem Solving - Basic and Circles - Problem Solving - Intermediate.

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