Let P and Q be points on the side AB of the triangleZPCQ =ZQCB, and let AD be the angle bisector of ZBAC. Line AD meetslines CP and CQ at M andN respectively. Given that PN = CD2ZBC A, prove that triangles CQD and QNB haveProblem 10.5ABC (with P between A and Q) such that ZACP =and 3ZBACthe same area.

Here we have to ise the concept of cyclic quadrilateral theorem. And after that we can apply…

Problem 10.5 Let P and Q be points on the side AB of the triangle ABC (with P between A and Q) such that ZACP = ZQCB, and let AD be the angle bisector of ZBAC. Line AD meets lines CP and CQ at M andN respectively. Given that PN = CD and 3ZBAC = 2ZBCA, prove that triangles CQD and QNB have ZPCQ the same area.

Problem 10.5 Let P and Q be points on the side AB of the triangle ABC (with P between A and Q) such that ZACP = ZQCB, and let AD be the angle bisector of ZBAC. Line AD meets lines CP and CQ at M andN respectively. Given that PN = CD and 3ZBAC = 2ZBCA, prove that triangles CQD and QNB have ZPCQ the same area.

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

Section6.4: Some Constructions And Inequalities For The Circle

Problem 11E: X, Y, and Z are on circle O such that mXY=120, mYZ=130, and mXZ=110. Suppose that triangle XYZ is...

See similar textbooks

Similar questions

Use Exercise 33 and the following drawing to complete the proof of this theorem: The length of the median of a trapezoid is one-half the sum of the lengths of the two bases. Given: Trapezoid ABCD with median MN Prove: MN=12(AB+CD) 33. Use Theorem 5.6.1 and the drawing to complete the proof of this theorem: If a line is parallel to one side of a triangle and passes through the midpoint of a second side, then it will pass through the midpoint of the third side. Given: RST with M the midpoint of RS;MNST Prove: N is the midpoint of RT
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._
Prove by the indirect method: Given: Scalene XYZ in which ZW bisects XZY point W lies on XY. Prove: ZW is not perpendicular to XY
X, Y, and Z are on circle O such that mXY=120, mYZ=130, and mXZ=110. Suppose that triangle XYZ is drawn and that the triangle ABC is constructed with its sides tangent to circle O at X, Y, and Z. Are XYZ and ABC similar triangles?
Given: Isosceles ABE with AEBE; also, D and C are midpoints of AE and BE, respectively. Prove: ABCD is an isosceles trapezoid. Exercises 17, 18
Given: RST, with XYRT and YZRS Prove: RXXS=ZTRZ
In O, chord AB chord CD. Radius OE is perpendicular to AB and CD at points M and N, respectively. If OE=13, AB=24, and CD=10, then the distance from O to CD is greater than the distance from O to AB. Determine how much farther chord CD is from center O than chord AB is from center O; that is, find MN.
Circles O, P, and Q are tangent as shown at points X, Y, and Z. Being as specific as possible, explain what type of triangle PQO is if: a OX=2,PY=3,QZ=1 b OX=2,PY=3,QZ=2
a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the triangle. Use the fact that the congruent diagonals of a rectangle bisect each other. Be sure to provide a drawing. bUse the relationship from part a to find CM, the length of the median to the hypotenuse of right ABC, in which mC=90, AC = 6, and BC = 8.