Question

The figure below shows a circle with chords AD and BC intersecting at point P.

Dennis took the measurements of the line segments and wrote them down as shown.

Segment PA is 1.6 cm, segment PB is 2.7 cm, segment PC is 2.4 cm, and segment PD is 4.8 cm.

Describe the method you use to prove that Dennis took incorrect measurements. Use geometric theorems to write a two-column proof.

Answer 1

@jim_thompson5910

Answer 2

Hint: use the intersecting chords theorem

http://www.mathopenref.com/chordsintersecting.html

Answer 3

ok i will check that out right now

Answer 4

How would i put that into a two-column proof?

Answer 5

well you could follow the same logic that is used to prove the theorem

but I'd just stick to the theorem itself if it were me

Answer 6

What would be the statement and what would be the justification?

Answer 7

hmm I think it would be 1 or 2 steps, but I guess that's probably too short

Answer 8

but you would use the fact that

PA*PD = PB*PC

Answer 9

Right, and thats justified by the intersecting chords theorem.

Answer 10

Thank You!

Answer 11

exactly