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11-72.

Prove that when two lines that are tangent to a circle intersect, the distances from the point of intersection to the points of tangency are equal. That is, in the diagram at right, when is tangent to at point , and is tangent to at point , prove that . Use either a
flowchart or a two‑column proof.

2 lines, intersecting at point, a. Top line is tangent to circle with center e, at point, d. Bottom line is tangent to circle, with center, e, at point, F. Line segments from, D, to, E, and from, E, to, F. Dashed line segment from, A, to, E.

Flow chart, 6 ovals: 1 flows to 2, 2, 3, & 4, flow to 5, which flows to 6. Labels: #1: AD, perpendicular to, DE, AF, perpendicular to, FE, Tangent is perpendicular to radius. #2: Angles, F, & D, are right angles, definition of perpendicular. #3: AE, = to, AE, segment is congruent to itself. #4: FE, = to, DE, all radii are congruent. #5: Triangle, ADE, congruent to triangle, AFG, by H,L, congruency #6: Segment, AD, congruent to segment, AF, congruent triangles give congruent parts.