3. An arc PQ of a circle of radius r is created with a central angle (in radians) as shown in the figure to the right. Assume the cen- ter of the circle is the origin of the Cartesian coordinate plane (so the point R lies on the x-axis). 0 r A(0) B(0) R O (a) Find the equations of lines tangent to the circle at P and Q (you should have three variables in your answer: x, the unspecified angle 0, and the unspecified radius r). (b) These two tangent lines intersect at a point R. Find it (your answer will also include and r).
3. An arc PQ of a circle of radius r is created with a central angle (in radians) as shown in the figure to the right. Assume the cen- ter of the circle is the origin of the Cartesian coordinate plane (so the point R lies on the x-axis). 0 r A(0) B(0) R O (a) Find the equations of lines tangent to the circle at P and Q (you should have three variables in your answer: x, the unspecified angle 0, and the unspecified radius r). (b) These two tangent lines intersect at a point R. Find it (your answer will also include and r).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Transcribed Image Text:3. An arc PQ of a circle of radius r is created
with a central angle (in radians) as shown
in the figure to the right. Assume the cen-
ter of the circle is the origin of the Cartesian
coordinate plane (so the point R lies on the
x-axis).
0
1
P
A(0) B(0) R
(a) Find the equations of lines tangent to the circle at P and Q (you should have three
variables in your answer: x, the unspecified angle 0, and the unspecified radius r).
=
(b) These two tangent lines intersect at a point R. Find it (your answer will also include
and r).
(c) P, Q, and R form a triangle as shown in the figure. What is the formula for the area of
this triangle, in terms of 0 and r?
(d) Recall that the formula for the area of a segment (piece of circle cut off from the rest
by a line segment PQ) is A(0) (0 sin). Let B(0) be the area between the line
p²
2
A(0)
segments PR, QR, and the arc PQ. Calculate lim
Ant B(A)
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