Hello, paupsers!

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(1) Prove: bisects

. . A radius drawn to the point of tangency is perpencidular to the tangent.

Hence, and are right triangles.

. . In a circle, all radii are equal.

. . Reflexive property

Hence: .

. . Side-side theorem for right triangles

Therefore: .

. . Corresponding parts of congruent triangles are equal.

(2) Prove: .

. . Corresponding parts of congruent triangles are equal.

(3) Prove: .

. . . They are radii.

. . . proved in (1)

Hence, is the perpendicular bisector of

. . Two points equidistant from the ends of a line segment determine the perpendicular bisector of the line segment.

Therefore: .