The tomahawk-shaped instrument shown in the accompanying gure can be used to solve the trisection problem. (PQ = QR = RS, with PTR a semicircle on PR as diameter, UR perpendicular to PS.) If LAOB is the angle to be trisected, place the tomahawk on the angle so that S lies on OA, the line segment UR passes through O, and the semicircle with diameter PR is tangent to OB at T. Prove that the triangles OTQ, ORQ, and ORS are all congruent, whence ZROA is one-third of LAOB. В T R 3 S A

The tomahawk-shaped instrument shown in the accompanying gure can be used to solve the trisection problem. (PQ = QR = RS, with PTR a semicircle on PR as diameter, UR perpendicular to PS.) If LAOB is the angle to be trisected, place the tomahawk on the angle so that S lies on OA, the line segment UR passes through O, and the semicircle with diameter PR is tangent to OB at T. Prove that the triangles OTQ, ORQ, and ORS are all congruent, whence ZROA is one-third of LAOB. В T R 3 S A

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 39E: The center of a circle of radius 2 in. is at a distance of 10 in. from the center of a circle of...

See similar textbooks

Similar questions

Draw an obtuse triangle and, by construction, find its orthocentre. HINT: You will have to extend the sides opposite the acute angles.
In trapezoid RSTV, RVST,mSRV=90, and M and N are midpoints of the nonparallel sides. a What type of triangle is RMN? b If ST = 13, RV = 17 and RS = 16, How long is RN? c What type of triangle is RVN? Hint: Use lengths of sides found in part b.
In O with diameter AC, OC=5 and AB=6. If M is the midpoint of BC, find AM.
Assuming that mBmA in , which diagonal AC-orBD- would be longer?
The center of a circle of radius 3 inches is at a distance of 20 inches from the center of a circle of radius 9 inches. What is the exact length of common internal tangent AB? HINT: Use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.
For coplanar points A,B, and C, suppose that you have used the Distance Formula to show that AB=5,BC=10, and AC=15. What can you conclude regarding points A,B, and C?
In ABC, M is the midpoint of AB and N is the midpoint of AC. If MN= 3x-11 and BC= 4x24, find the value of x._
In O with diameter AC, OC=5 and AB=6. If M is the midpoint of BC, find AM. _
In P, whose radius has length 8in., mAB=mBC=60. Because mAC=120 chord AC is longer than either of the congruent chords AB and BC. Determine how much longer AC is than AB; that is, find the exact value and the approximate value of ACAB.
The cylindrical brush on a vacuum cleaner is powered by an electric motor. In the figure, the drive shaft is at point D. if mAC=160, find the measure of the angle formed by the drive belt at point D; that is find mD
The center of a circle of radius 2 in. is at a distance of 10 in. from the center of a circle of radius length 3 in. To the nearest tenth of an inch, what is the approximate length of a common internal tangent? Use the hint provided in Exercise 38. HINT: use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.
Use the results from Exercises 36 and 37 to find the exact length of the radius of the inscribed circle for a triangle with sides of lengths a 8, 15 and 17 b 7, 9 and 12