Plane And Solid Geometry : With Problems And Applications

Cover Plane And Solid Geometry : With Problems And Applications
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Given two concentric circles whose radii are r and r' the length of a chord of the greater which is tangent smaller.
34. If two equal circles of radius r intersect so that each passes through the center of the other, find the length of the common chord.
35. The square on the hypotenuse of a right triangle is four times the square on the altitude upon the hypotenuse. Prove it isosceles.
36. In a right triangle the hypotenuse is 10 feet and the difference between the other sides is 2 feet. Find t
...he sides. , 37. Two equal circles are tangent to each other and each circle is tangent to one of two lines perpendicular to each other. Find the locus of the points of tangency of the two circles.
Suggestion. Note that the point of tangency bisects their line of centers and that the centers move along lines at right angles to each other.
38. The square on a diagonal of a rectangle is equal to half the sum of the squares on the diagonals of the squares constructed on two adjacent sides of the rectangle.


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