Circumference

[Jean2003]

A center circumference C, inscribed at a right angle XÔY, tangents OX into D. A half-straight O origin, internal to angle XÔY, intersects circumference C at points A and B, such that arc AD is half of arc BD . Calculate the angle BOD



The answer is 15º

 

[Dr.Peterson]

Your English is not quite right, so I'm not sure what it means. Here is a guess:

A circle with center [MATH]C[/MATH] is inscribed in a right angle [MATH]\widehat{XOY}[/MATH]; [MATH]OX[/MATH] is tangent to the circle at [MATH]D[/MATH]. A ray from the origin [MATH]O[/MATH], internal to angle [MATH]\widehat{XOY}[/MATH], intersects the circumference of circle [MATH]C[/MATH] at points [MATH]A[/MATH] and [MATH]B[/MATH], such that arc [MATH]AD[/MATH] is half of arc [MATH]BD[/MATH]. Calculate the angle [MATH]\widehat{BOD}[/MATH].​

Is that right?

Next, we need to know what you have learned that you can use to solve the problem; the best way to do that is to show some attempt to solve it, showing us what ideas you have even if they are wrong. It can also be helpful to tell us what theorems you have most recently learned.

When you submit a question like this from another language, it can be helpful to show the original along with your translation, which can help us figure out how to improve your translation (even if we don't know the language).

 

[Jean2003]

Thanks and sorry, I don't speak English very well. I am from Brazil and have not found the correct answer to this question on my country websites

 

[Jean2003]

I have learned arcs and rope of a circumference

 

[tkhunny]

* chords

not "ropes".

 

[Dr.Peterson]

Thanks and sorry, I don't speak English very well. I am from Brazil and have not found the correct answer to this question on my country websites

I have learned arcs and [chords?] of a [circle?]

Do you know the theorems about angles between chords, secants, and tangents, as shown here? They will be useful, especially the very last one. This page will also show you some of the correct words to use.