IA Activity I Introduction and purpose of task: The goal of this task is always to investigate the positions of points in intersecting groups and to uncover the various relationships between stated circles. Ring C1 features center Um and radius r. Circle C2 features center P and radius OP.
Permit A be one of the parts of intersection of C1 and C2. Circle C3 provides center A and radius r (therefore circles C1 and C3 are the same size). The point P’ (written P prime) is a intersection of C3 with OP. This is certainly shown in the diagram listed below.
Analytically discover OP’ employing r=1 and OP=2, OP=3, and OP=4: First, I actually created a collection (see the dashed collection in the over figure) between AP’ that creates the? AOP’. Because P’ can be on the area of group of friends C3 and A may be the center of circle C3, that means that AP’ is definitely equal to the radius of C3, which is 1 . We also know that because line AO connects the area of C1 with the centre of C1 (O) as well as the circumference of C3 together with the center of C3 (A), the radii of these groups is the same, which means that they are really equivalent circles.
Therefore , inside the? AOP’, AO=AP. When a triangular has two equivalent sides, it is an isosceles triangle. By that logic,? O=? P’. Now, My spouse and i looked at the triangle that is certainly already used the above figure,? AOP. We know that this triangle is also isosceles because OP=AP. By that logic,? A=? O. Making use of the law of cosines c^2=a^2+b^2-2abcos(C), which works for any triangle, I assigned? to? U and determined that cos(? )=1/(2*OP). Then simply, using the law of sines (insert rules of sines here), sin(? )/1=sin(180-2? )/OP’ OP’=sin(180-2? /sin(? ) OP’=sin(2? )/sin(? ) OP’=2cos(? ) But since cos(? )=1/2OP as before discovered, OP’=1/OP By using this equation, I derived the following answers analytically using r=1 and OP=2, OP=3, and OP=4. OP234 OP’0. 50. 330. 25 Tendencies of intersecting circles and general assertion describing conversation that occurs when value of OP is changed: As OP changes, the resulting OP’ value diminishes exponentially. This kind of shows that ______________ BLAH BLAH BLAH BLAH BLAH Analytically find OP’ using OP=2 and r=2, r=3, and r-4:
Behavior of intersecting circles and general affirmation describing discussion that occurs when value of OPERATIVE is improved: Comments about consistency of general affirmation #1 versus general assertion #2: Use technology to review other principles of l and OPERATIVE. Find the typical statement intended for OP’: Evaluation the validity of the most recent general statement by using several values of OP and r: Discussion of scope and limitations of the extremely recent standard statement: Description of how standard statement was arrived at: Further more comments: Additional investigation in to relationships of intersecting circles:
