Triangle inscribed within a circle

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Homework Help Overview

The problem involves a triangle ABC inscribed in a circle, where the diameter AC is one side of the triangle. The discussion centers around the relationship between the angles of the triangle and the arcs they subtend in the circle.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the properties of inscribed angles and their relationship to the arcs they subtend. Questions arise regarding the measurement of these angles and the implications of having a side as the diameter of the circle.

Discussion Status

Some participants have provided insights into the properties of angles subtended by arcs, while others are seeking clarification on the concepts involved. There is a mix of understanding and uncertainty regarding the angle measures and their relationships.

Contextual Notes

Participants note the assumption that one side of the triangle is the diameter of the circle, which influences the angle measures being discussed. There is also mention of varying levels of familiarity with the topic among participants.

BrownianMan
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ABC inscribed within a circle whose diameter AC forms one of the sides of hte triangle. If Arc BC on the circle subtends an angle of 40 ddegrees, find the measure of angle BCA within the triangle
 
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What's your idea ?
Any drawing ?
 
I haven't done this kind of thing since high school. Could you explain how you measure inscribed angles? My initial guess is that one of the sides is 90, one 40, and the other must be 50...
 
Yes that's right. Because whenever you have a triangle with one of its sides being the diameter of the circle, then the opposite angle to that side will be 90o.
 
If angle A has its vertex on a circle and subtends an arc of \theta degrees, then the measure of the angle is \theta/2 degrees. You are given that one angle of the triangle subtends an arc of 40 degrees and another an arc of 90 degrees.
 

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