The square of a tangent segment from an external point will be equal to the product of the two segments of a secant of a circle through the point. This important relation between tangent segments and secant of a circle is explored.
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Basic concepts in Geometry
Incentre ratio is Segmentation ratio of angle bisectors at incentre. An internal angle bisector also segments opposite side in ratio of two adjacent sides.
Law of sines and cosines relate side with sine and cosine of an angle opposite the side in triangle. By sine law, ratios of side to sine of angle are equal.
Centroid divides triangle area into 3 equal parts formed by the longer median segments at centroid and 6 equal parts by all six median segments at centroid.
Relation between median and sides of triangle: Sum of two sides is larger than the median from common vertex and three times sum of squares of length of sides equals four times the squares of medians of a triangle.
Arcs and subtended angles: Any arc in a circle will subtend an angle at the centre twice the angle it subtends at any point on its complementary arc.
Circle basic concepts: Chords, arcs, tangents, cyclic quadrilateral, angle subtended by a chord and secant of a circle with examples and exercise.
Quadrilateral basic Concepts: Properties of a quadrilateral, polygons, squares, parallelograms, rhombus, cyclic quadrilateral with examples and exercise.
Geometry basics points lines and triangles: Straight lines, parallel lines, angles, triangles, properties of triangles with examples and exercise.