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A-Math: This Plane Geometry Question Almost Drives Me To Insanity!


Plane geometry is one of the top killer questions in A-Math as there are many things to prove in addition to the many lines, circles, triangles, angles ...

Read about the post I wrote earlier What you need to know to do well in Plane Geometry Part 1

I must admit this question almost drives me to insanity ;-) but luckily I saw the light when I was on the verge of sane and insanity ...

Question: Prove that a circle can be drawn passing through the points T,P,X and Q. [3 marks]

planegeometry-circle

Let me know how you handle this question in the comments section. For those who wants the step by step solution, drop me a comment as well. I highly recommend that you think about this question first before asking for solution.

There are 2 strategies I have used to help me in this Plane Geometry question. Do you want to know? so that you can learn and use them in your own question.

Hint: You must use one of the properties of circles.

Update: Video solution Here

Ai Ling Ong

Hi, I'm Ai Ling Ong. I enjoy coaching students who have challenges with understanding and scoring in 'O' Level A-Maths and E-Maths. I develop Math strategies, sometimes ridiculous ideas to help students in understanding abstract concepts the fast and memorable way. I write this blog to share with you the stuff I teach in my class, the common mistakes my students made, the 'way' to think, analyze... If you have found this blog post useful, please share it with your friends. I will really appreciate it! :)

Filed Under: A-Maths Tuition, Learning Tools, Weekly Question Tagged With: plane geometry, property of circle, shortcut

Reader Interactions

Comments

  1. Hong says

    October 7, 2008 at 11:50 pm

    I really donno, haha, so can you show the solutions?

  2. anjali says

    October 9, 2008 at 12:16 am

    As PT and PQ are of equal length, PTQ is an isosceles triangle, thus the circle can be drawn passing through these points by circumscribing the triangle....

  3. Sean Chua says

    October 9, 2008 at 8:30 pm

    Hi Always Lovely,

    This one is indeed tough...yet to come out with my answers..

    Rgds
    Sean

  4. TK says

    October 10, 2008 at 9:05 pm

    Hmm this question is difficult, don't even know where to start. Mind revealing the solution?

  5. Joscelin says

    October 11, 2008 at 5:49 pm

    to add on my previous reply:QXPT is a cyclic quad because the opp <s = 180degrees...

    hmm if its wrong may i have the solution :)

  6. Joscelin says

    October 11, 2008 at 5:50 pm

    <QXT = <QPT
    <XQP = <XTP
    <s in the same segment

    sorry for double reply! :)

  7. alwaysLovely says

    October 12, 2008 at 5:07 am

    @anjali: As this is a 3 marks proving question, you won't get the full marks by stating the property of triangle PTQ. Nevertheless. good attempt :)

    @Joscelin: Joscelin, you can't begin with the circle already passes through the 4 points and make the conclusions as above. You have to prove your conclusions to be correct hence the 4 points pass through the circle. This is also the challenginng part of many students for a proving question but you got the main concept correct. Begin the proving with the fact that angles in the same segment are equal.

    I have updated the solution here => https://www.singaporeolevelmaths.com/2008/10/11/video-solution-of-plane-geometry-question-plusstrategy-to-handle-angles/

  8. J says

    July 24, 2009 at 4:43 pm

    Angles XPT = Angles XQT = 90(tangent perpendicular to radius)

    Using the property, Angles in a semicircle, a circle passing thru T, P, X and Q can be constructed with XT as a diameter.

  9. Mohamed Renzie says

    December 6, 2011 at 7:24 pm

    angle xtq=rqz(corresponding angles)
    but,angle rqz=rpq(angles in the alternate segment)
    .:.angle xtq=rpq
    .:.xpq=rpq

Trackbacks

  1. singaporeolevelmaths | Video Solution Of Plane Geometry Question (Plus:Strategy To Handle Angles) says:
    October 11, 2008 at 7:09 pm

    [...] Comments Joscelin on A-Math: This Plane Geometry Question Almost Drives Me To Insanity!Joscelin on A-Math: This Plane Geometry Question Almost Drives Me To Insanity!TK on A-Math: This [...]

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