Modern geometry . triangle of given shape and size always passthrough two fixed points, the third side always touches a fixed circle. [The centre of this circle lies on the locus of the vertex of the triangle,and its radius is equal to an altitude of the triangle.] Ex. 379. If two sides of a triangle of given shape and size slide alongtwo fixed circles, the envelope of the third side is a circle. [BobilliersTheorem.] CHAPTEE X. THE RADICAL AXIS; COAXAL CIRCLES. Ex. 380. Draw a pair of circles intersecting at points P and Q; fromany point on PQ produced draw tangents to the circles; prove that
Modern geometry . triangle of given shape and size always passthrough two fixed points, the third side always touches a fixed circle. [The centre of this circle lies on the locus of the vertex of the triangle,and its radius is equal to an altitude of the triangle.] Ex. 379. If two sides of a triangle of given shape and size slide alongtwo fixed circles, the envelope of the third side is a circle. [BobilliersTheorem.] CHAPTEE X. THE RADICAL AXIS; COAXAL CIRCLES. Ex. 380. Draw a pair of circles intersecting at points P and Q; fromany point on PQ produced draw tangents to the circles; prove that thesetangents are of equal length. Definition. The locus of the points from which tangentsdrawn to two circles are equal is called the radical axis of thetwo circles. In Ex. 380, we have seen that in the case of two intersecting circles anypoint on their common chord produced is on their radical axis. This is aparticular case of the following theorem. Theorem radical axis of two circles is a straight fig. 49. 88 THE EADICAL AXIS
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