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O is the center of a circle whose circumference passes through the vertices of an equilateral triangle ABC. If P is any point taken on the circumference and AD, BE, CF are three perpendiculars from A, B, C on the tangent from P to the circle, show that the sum of these perpendiculars is equal to twice the altitude of the ABC. Draw AM BC; then produce it to meet the circle in N. Draw the perpendiculars MK, NL on the tangent from P and join OP

O is the center of a circle whose circumference passes through the vertices of an equilateral triangle ABC. If P is any point taken on the circumference and AD, BE, CF are three perpendiculars from A, B, C on the tangent from P to the circle, show that the sum of these perpendiculars is equal to twice the altitude of the ABC. Draw AM BC; then produce it to meet the circle in N. Draw the perpendiculars MK, NL on the tangent from P and join OP

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter4: Quadrilaterals
Section4.3: The Rectangle, Square, And Rhombus
Problem 42E: a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three...
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O is the center of a circle whose circumference passes through the vertices of an equilateral triangle ABC. If P is any point taken on the circumference and AD, BE, CF are three perpendiculars from A, B, C on the tangent from P to the circle, show that the sum of these perpendiculars is equal to twice the altitude of the ABC. Draw AM BC; then produce it to meet the circle in N. Draw the perpendiculars MK, NL on the tangent from P and join OP
Transcribed Image Text:O is the center of a circle whose circumference passes through the vertices of an equilateral triangle ABC. If P is any point taken on the circumference and AD, BE, CF are three perpendiculars from A, B, C on the tangent from P to the circle, show that the sum of these perpendiculars is equal to twice the altitude of the ABC. Draw AM BC; then produce it to meet the circle in N. Draw the perpendiculars MK, NL on the tangent from P and join OP
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