(A chord of givenlength). Given is a circleC with centerO, a pointP inside the c
ID: 2939427 • Letter: #
Question
(A chord of givenlength). Given is a circleC with centerO, a pointP inside the circleand a chord AB. Construct a chord congruent to AB through point P anddescribe yourconstruction by construct all solutions—none, one or two—andexplain how you decide which case occurs plus draw examples for allthree cases. Thanks, I'll rate the bestever! (A chord of givenlength). Given is a circleC with centerO, a pointP inside the circleand a chord AB. Construct a chord congruent to AB through point P anddescribe yourconstruction by construct all solutions—none, one or two—andexplain how you decide which case occurs plus draw examples for allthree cases. Thanks, I'll rate the bestever! Thanks, I'll rate the bestever!Explanation / Answer
I'll give you a verbal description, from which I hope you willbe able to complete the construction. Construct the circle withcenter O and radius OP. There are 3 cases: 1. The circle does not intersect chord AB. In this case, thereis no solution. Any chord through P is longer than AB. 2. The circle intersects AB at exactly one point. In thiscase, there is exactly one solution. As the circle is tangent tothe chord, the chord is perpendicular to the radius to the point oftangency. A congruent chord will be the same distance from O, soconstruct OP, construct its perpenducular at P. The chord collinearwith the perpendicular is the solution. 3. The circle intersects AB at two points. Then there are twosolutions. Choose one of the intersection points, denoting it C.Then using radius AC and center P, construct circle P. It willintersect circle O at two points. Each solution is the chordthrough one of the points and P.Related Questions
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