Geom2 nov 28 - PEM Level C 28 November 2009 Topics in...

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PEM Level C 28 November 2009 Topics in Geometry - Chords, Tangents and Intersecting Circles Examples: 1. In a circle, chord AB is bisected at E by chord CD . If CE = 16 and ED = 4, find the length of chord AB . 2. An arch is built in the form of an arc of a circle and is subtended by a chord 30 feet long. If a chord 17 feet long subtends half the arc, what is the radius of the circle? 3. Let AB be the diameter of a semicircle of radius 2. Let C and D be two points on the semicircle such that AD = DC = 1. Find BC . 4. Three circles, centered at A , B and C , respectively, are externally tangent to each other. Find the radii of the circles if AB = 7, AC = 5 and BC = 9. 5. Two tangents to a circle are at right angle with each other. There is a point on the shorter arc of the circle between the two points of tangency that is 4.5 cm away from one tangent and 4 cm away from the other. Find the radius of the circle. 6. Two circles C 1 and C 2 are tangent externally to each other, and let P be a point outside both circles. Prove that the tangents drawn to the circles from
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