# Geometry

I want a problem about circles, tangents, secants and inscribed angles. Please create some questions and problems! thank you!

Note by Kheena Medina
3 years, 9 months ago

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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 $$\angle DAC=\angle ABC$$

- 3 years, 9 months ago

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.

- 3 years, 9 months ago

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

- 3 years, 9 months ago

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

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

- 3 years, 9 months ago

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

- 3 years, 9 months ago

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

Staff - 3 years, 9 months ago