C Q18 anion mun SO TO COO D 0% sail od bas sya syd bezolons non R In the diagram above OC = = c and OĎ=d. The points P and Q lie on OC and OD produced respectively, so that OC : CP= 1:2 and OD: DQ = 2:1. The line CD is extended to R so t CD= DR. (i) Find, in terms of c and/or d, the vectors OP, OO and OR. (ii) Show that the points P, Q and R are collinear and find the ratio PQ: QR.

C Q18 anion mun SO TO COO D 0% sail od bas sya syd bezolons non R In the diagram above OC = = c and OĎ=d. The points P and Q lie on OC and OD produced respectively, so that OC : CP= 1:2 and OD: DQ = 2:1. The line CD is extended to R so t CD= DR. (i) Find, in terms of c and/or d, the vectors OP, OO and OR. (ii) Show that the points P, Q and R are collinear and find the ratio PQ: QR.

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 37E: Given: AB is an external tangent to O and Q at points A and B; radii lengths for O and Q are 4 and...

See similar textbooks

Similar questions

Given: AB is an external tangent to O and Q at points A and B; radii lengths for O and Q are 4 and 9. Find: AB HINT: The line of centers OQ contains point C, the point at which O and Q are tangent.
The point mid ay between (a, b) and (c, d) _____________. So the point midway between (1, 2) and (7, 10) is ___________.
Line l is parallel to plane P that is, it will not intersect P even if extended. Line m intersects line l.What can you conclude about m and P?
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
The center of a circle of radius 2 inches is at a distance of 10 inches from the center of a circle of radius length 3 inches. 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.
Complete an analytic proof of the following theorem: In a triangle that has sides of lengths a,b, and c, if c2=a2+b2, then the triangle is a right triangle.