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 \(\angle DAC=\angle ABC\)
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Michael Mendrin
·
2 years ago

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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 Mendrin
·
2 years ago

@Ali Caglayan
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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

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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 \(\angle DAC=\angle ABC\) – Michael Mendrin · 2 years ago

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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. – Michael Mendrin · 2 years ago

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– Ali Caglayan · 2 years ago

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

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. – Michael Mendrin · 2 years ago

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– Ali Caglayan · 2 years ago

Hehe I didn't read the note at the bottom of the question. Ooops. Back to the whiteboard.Log in to reply

Check out the problems in Circles - Problem Solving - Basic and Circles - Problem Solving - Intermediate. – Calvin Lin Staff · 2 years ago

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