Point 9 of 10 — Unit 2: Similarity of Polygons and Triangles, Areas and Circle TheoremsQuestion bank: 0 questions (0 with pictures)
092-9 Similarity inside the circle
Two intersecting chords
If chords AB and CD meet at an interior point E, then △AEC ~ △DEB (vertically opposite angles at E and angles in the same segment standing on arc CB), and EA × EB = EC × ED.
Two secants from an external point
From a point M outside the circle, two secants cut the circle at A, B and C, D where A and C are the nearerpoints and B and D thefartherones: MA × MB = MC × MD.
Tangent and secant from an external point
When the second secant collapses onto the tangent (C = D = T) the result becomes MT² = MA × MB — the square of the tangent equals the product of the segments of the secant.
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