How Much Do You Know About Geometry?

Geometry Level 4

Consider the following statements.

[ 1 ] [1] . The converse of Ptolemy's Theorem isn't always true.

[ 2 ] [2] . If a trapezium [a convex quadrilateral with at least one pair of sides parallel] is cyclic, then its legs are always equal.

[ 3 ] [3] . The lowest value of a power of a point is 0 0 .

Which of these are correct?

This problem is from the set "MCQ Is Not As Easy As 1-2-3". You can see the rest of the problems here .

Only [ 2 ] [2] None of them are correct. All of them are correct. Only [ 3 ] [3]

Mursalin Habib by Mursalin Habib , 23, Bangladesh

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

Krishna Ar
May 13, 2014

Simple question. Thanks @Mursalin Habib - The first part is obviously false and the second is 100% true. W.R.T third one, I don't know what it is. Eliminating incorrect options leaves us with only (2). I would be grateful if someone explains what the third part means to me. Thanks

2 Helpful 0 Interesting 0 Brilliant 0 Confused

From what i know the power of a point can be positive, zero and negative that's why it's wrong.

And also, power of a point was used to prove secant-tangent and secant-secant

One way of computing it is by subtracting the distance of any point from the center of the circle to the radius of the circle.

From that statement we can conclude that

  • If the point chosen is outside of the circle, the difference will be positive

  • If the point is in the circle, it will be zero because it will also be a radius

  • If the point is inside the circle, it will be negative

Marc Tomagos - 7 years ago

Log in to reply

Thank you very much :)

Krishna Ar - 7 years ago

Plz xpln why the Ist part is correct. u jst stated your solution.nd also i ned 2 undrstnd wht d 2nd prt means.

Chandrachur Banerjee - 7 years, 1 month ago

Log in to reply

Of course, you know that Ptolemy theorem's converse stands true. And a cyclic trapezium is isosceles is again a provable theorem ( Try it, its fun :) )...Thus You arrive at what you desired. PLZ upvote my solution if u found it good ... Btw how did u solve it ? o.O

Krishna Ar - 7 years, 1 month ago
Rohan Arora
May 24, 2014

just visualize it

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Kevin Patel
May 15, 2014

Easy one again, a part of visual geometry.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...