Question

Two circles are given in a plane.
State the conditions under which there is a common tangent line to
both.

Explain how to construct the common tangent. Prove that your
construction is correct.

Answer #1

Conditions under which there is a common tangent line to both the circles are:

1. When two circles touch each other internally 1 **common
tangent** can be drawn to the circles
i.e. |r_{1} - r_{2}| =
c_{1}c_{2}

2. When two circles intersect in two real and distinct points, 2
**common tangents** can be drawn to the circles i.e.
|r_{1} - r_{2}| < c_{1}c_{2}
< r_{1} + r_{2}

3. When two circles touch each other externally, 3
**common tangents** can be drawn to the circles
i.e. r_{1} + r_{2} =
c_{1}c_{2}

4. When two circle neither touch nor intersect and one lies
outside the other, then 4 common tangents can be drawn
i.e. r_{1} + r_{2} <
c_{1}c_{2}

Prove that when the distance between the centers of two circles
is greater than the sum of the radii, the circles have four common
tangents. The midpoints of these four line segments are
collinear.
My teacher did not mention any thing about tangent lines. That
is all for the question.

For the following, give constructions using a straightedge and a
compass with memory. You must prove that your construction
works.
Construct a circle tangent to two given circles and having a
radius equal to the length of a given line segment. Assume that the
given line segment is long enough to make this possible.

State two conditions under which an environmental economist
might not recommend an emissions trading program as an attractive
environmental policy instrument. Explain your reasoning in each
case.

Sorry the question is :
Prove the following statement: Given two non-concentric circles,
the center of an orthogonal circle to both circles lies on the
radical axis of them.

State which hypothesis test would be appropriate under the
following conditions. We know that our two data sets come from
approximately normally distributed populations and that they have
very different variances.
The Answer Options are:
2-sample t-test with unequal variances
2-sample t-test with equal variances
t-test Mann-Whitney
U Test
z-test

Consider two particles moving in the xyxy-plane according to
parametric equations.
At time tt, the position of particle A is given by x(t) = 2t-3,
y(t) = t^2-3t-5x
Let kk be some real number. At time tt, the position of particle
B is given by x(t) = 4t+3, y(t) = 2t+k^2x
Think about the curve traced out by the movement of particle A.
Find the equation of the tangent line to the curve at t=4t=4. Give
your answer in slope-intercept...

Analyze the behavior of capacitors under steady state direct
current and high frequency AC current (500 Hz) as both a sine wave
and square wave. Explain how capacitors behave under these
conditions in your intro!

using these axioms ( finite affine plane ) :
AA1 : there exists at least 4 distinct points , no there of
which are collinear .
AA2 : there exists at least one line with n (n>1) points on
it .
AA3 : Given two distinct points , there is exactly one line
incident with both of them .
AA4 : Given a line l and a point p not on l , there is exactly
one line through p...

Which of the following phosphorous trihalides is most likely a
gas(under the same conditions at normal pressure and temperature)?
a) PF3, b) PCl3, c) PBr3, d) PI3, e) this cannot be determined. The
answer given is a) PF3. How is this determined? Please explain!
Thank you

Indicate which direction the reaction at equilibrium should
shift under the given conditions for the reaction of PCl3(g) +
Cl2(g) ⇌ PCl5(g).
addition of PCl3
addition of Cl2
addition of PCl5
removal of PCl3
removal of Cl2
removal of PCl5
decrease the volume of the container
addition of Ne
Indicate which direction the reaction at equilibrium should
shift under the given conditions for the exothermic reaction of
H2(g) + CO2(g) ⇌ H2O(g) + CO(g).
addition of CO2
addition of H2O...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 45 minutes ago

asked 46 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago