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Let ABC be a triangle for which the tangent from A to the circumcircle intersects line BC at D, and let O be the circumcenter. Construct the line that passes through A and is perpendicular to OD. & intersects OD at E and BC at F. Let the circle passing through ADO intersect BC again at H. It is given that AD = AO = 1. A (a) Find OE. = (b) Suppose for this part only that FH determine the area of triangle √12 OEF. (c) Suppose for this part only that BC = √3: determine the area of the triangle OEF. (d) Suppose that B lies on the angle bisector of DEF. Find the area of the triangle OEF.

Let ABC be a triangle for which the tangent from A to the circumcircle intersects line BC at D, and let O be the circumcenter. Construct the line that passes through A and is perpendicular to OD. & intersects OD at E and BC at F. Let the circle passing through ADO intersect BC again at H. It is given that AD = AO = 1. A (a) Find OE. = (b) Suppose for this part only that FH determine the area of triangle √12 OEF. (c) Suppose for this part only that BC = √3: determine the area of the triangle OEF. (d) Suppose that B lies on the angle bisector of DEF. Find the area of the triangle OEF.

Elementary Geometry for College Students
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter10: Analytic Geometry
Section10.CT: Test
Problem 1CT
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Let ABC be a triangle for which the tangent from A to the circumcircle intersects line BC at D, and let O be the circumcenter. Construct the line that passes through A and is perpendicular to OD. & intersects OD at E and BC at F. Let the circle passing through ADO intersect BC again at H. It is given that AD = AO = 1. A (a) Find OE. = (b) Suppose for this part only that FH determine the area of triangle √12 OEF. (c) Suppose for this part only that BC = √3: determine the area of the triangle OEF. (d) Suppose that B lies on the angle bisector of DEF. Find the area of the triangle OEF.
Transcribed Image Text:Let ABC be a triangle for which the tangent from A to the circumcircle intersects line BC at D, and let O be the circumcenter. Construct the line that passes through A and is perpendicular to OD. & intersects OD at E and BC at F. Let the circle passing through ADO intersect BC again at H. It is given that AD = AO = 1. A (a) Find OE. = (b) Suppose for this part only that FH determine the area of triangle √12 OEF. (c) Suppose for this part only that BC = √3: determine the area of the triangle OEF. (d) Suppose that B lies on the angle bisector of DEF. Find the area of the triangle OEF.
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