menu
bartleby
search
close search
Hit Return to see all results

Suppose that the lines AB and CD intersect at a point P such that PA PB PC PD andsuch that A is between points P and B, and C is between points P and D. Prove thatpoints A, B,C,D are on one circle. You are encouraged to usepropositions from Books 1, 2, 3,& 4 from Euclid's Elements. Draw apicture to help support your proof.

Question
Suppose that the lines AB and CD intersect at a point P such that PA PB PC PD and
such that A is between points P and B, and C is between points P and D. Prove that
points A, B,C,D are on one circle. You are encouraged to use
propositions from Books 1, 2, 3,
& 4 from Euclid's Elements. Draw a
picture to help support your proof.
help_outline

Image Transcriptionclose

Suppose that the lines AB and CD intersect at a point P such that PA PB PC PD and such that A is between points P and B, and C is between points P and D. Prove that points A, B,C,D are on one circle. You are encouraged to use propositions from Books 1, 2, 3, & 4 from Euclid's Elements. Draw a picture to help support your proof.

fullscreen
check_circleAnswer
Step 1

Given that the lines AB and CD intersects at a point P such that

РАРВ - РC.PD
help_outline

Image Transcriptionclose

РАРВ - РC.PD

fullscreen
Step 2

Since, there is a theorem that, “A circle always passes through three non-collinear points.”

So, draw the circle through three non-collinear points A, B and C and suppose that point D is not on the circle.

Then two cases are arising,

Case 1: When the point D is outside the circle, then the line CD intersects the circle at D’ as shown in the following diagram,

P
help_outline

Image Transcriptionclose

P

fullscreen
Step 3

By the diagram AP.PB=CP.PD’

But given that PA.PB=PC.PD

Then supposition t...

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in

Math

Advanced Math

Related Advanced Math Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: 1. The Greek mathematician Menaechnus (350 B.C.) obtained a purely theoretical solu- tion to the dup...

A: To justify Manaechnus's geometric method to solve "dublication of cube" problem

question_answer

Q: For the following collection of sets, define a set An for each n an element of N such that the index...

A: Click to see the answer

question_answer

Q: Please help me number 6. Thanks!

A: We are given that the unit vectors x, y, z satisfies the equationTo find the relation between the re...

question_answer

Q: Mechanical vibrations(differential equations) problem: A mass weighing 4 pounds is attached to a spr...

A: Let m be the mass attached, k be the spring constant and let b be a positive damping constant.Then, ...

question_answer

Q: X The cost in dollars y of producing x computer desks is given by y 30x +6000 a. Complete the table ...

A: a.The given function is

question_answer

Q: I need help with the rules for finding the difference quotient. for example. f(x)= 1/x^2

A: To evaluate the difference quotient for the given function

question_answer

Q: Mail Tucker, Ge x b Login | bartleby BB MyLab Math - R X lc Wait for Next Q X Limiting Reactan WA4.d...

A: Suppose T: R3→R3 is a linear transformation and {v1, v2, v3} be the linear dependent vectors in R3 t...

question_answer

Q: Determine whether each of the following is a subspace of the parent vector space. The set of polynom...

A: To determine whether the given subsets are subspaces

question_answer

Q: 2 How many subintervals does the composite trapezoid rule need to obtain the approximation of the fo...

A: Given function is 

Sorry about that. What wasn’t helpful?