I found that AOB is 90° and thus, AB is √2. Doctor Rick’s work, as suggested, involved a triangle similar to one from last week’s problem, but that is not the only way. See what you can do now.ĭrawing in the radii, as I already did above, is a standard first step, as they must be involved in the solution. The most challenging may bring to mind one of the problems we have discussed with you before.
#HOW TO TYPE A CIRCLE WITH A LINE THROUGH IT HOW TO#
Many of the angles you will now find in these three triangles will be familiar angles that you know how to work with. This is another interesting problem!Īs a start, I suggest constructing the radii OA, OB, and OC, and determining the interior angles of the triangles AOB, BOC, and COA. Since all we were given was the problem, Doctor Rick responded with just a hint, and the usual request to see work: With no formula for this radius, and no trigonometry, how are we to do this? Using trigonometry, we could find the sides if we knew one of them but the only length we have is the circumradius (the radius of the circumscribed circle). Here is a picture showing all the information we have: When a = 75°, b = 60°, c = 45° and r = 1, the length of sides AB, BC, and CA are calculated as _, _, _ without using trigonometric functions. The angles of the triangle are CAB = a, ABC = b, BCA = c. Here is the new problem, from the very end of last December:Ī circle O is circumscribed around a triangle ABC, and its radius is r. Finding the sides of a triangle in a circle It also illustrates a situation where different methods can lead to what appear to be entirely different answers, yet they may be identical. As we enjoy doing, we led the student through several possible approaches to a solution. Not long after that question, the same student, Kurisada, asked a question about triangle inscribed in a circle, which had some connections to the other.
Last week we looked at a question about a triangle inscribed in a semicircle.
0 kommentar(er)
