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, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter6: Circles

Section6.3: Line And Segment Relationships In The Circle

Problem 5E: Sketch two circles that have: a No common tangents b Exactly two common tangents c Exactly three...

See similar textbooks

Similar questions

If x ¡s positive and y is negative, then the point (x , y) is in Quadrant ____________.
Use the information given in Figure 1 to find x, h, s, and r if y=3. (Note: s is the distance from A to D. and y is the distance from D to B .)
Sketch two circles that have: a No common tangents b Exactly two common tangents c Exactly three common tangents d Exactly three common tangents e Exactly four common tangents
For the 30-60-90 triangle shown, suppose that XY=2a. Find: a XZ b YZ
Show construction lines and arcs for each of these exercises. Trace each circle and point in Exercises a through c and construct tangents to the circles from the given points.
Refer to the following figure in answering Exercises 7 through 13. It may be helpful to sketch figures.When side x= side y. a. What is the value of 1 ? b. What is the value of the tangent function? c. What is the value of the cotangent function?
Given: XYZ with angles as shown in the drawing Find: XY HINT: Compare this drawing to the one for Exercise 20.
Find the distance between P and Q. P(3,7);Q(6,3)
Give the coordinates of each point A, B, C, D, and E. Also name the quadrant in which each point lies.
Sketch the curve represented by each set of equations by eliminating the parameter. a. x=5cos and y=3sin,02 b. x=1+tan and y=2+2sec,/23/2