[EM20151129CGCB] Bisector of a Chord in a Circle

Problem

Introduction

     This “elementary” mathematics question poses a challenge because it actually testing Coordinate Geometry and Circle Geometry.  In the setting of tests and exams, there seems to be a trend of combining topics.  To solve this problem successfully, students need to know that when a chord is bisected (cut into two equal parts), the line segment joining its mid-point to the centre of the circle will be perpendicular to the chord itself.  Thereafter, we can proceed with Pythagoras’ Theorem.

Solution

Remarks

     There is actually no boundary between topics and even subjects.  Things to be learned are separated into topics only to facilitate teaching of the material.  Students are encourage to adopt a more wholistic view of knowledge.

Heuristics Used

H04. Look for pattern(s)

H05. Work backwards

H09. Restate the problem in another way

H10. Simplify the problem

H11. Solve part of the problem

H13* Use Equation / write a Mathematical Sentence

Suitable Levels

* GCE ‘O’ Level Mathematics (“Elementary Mathematics”)

* GCE ‘O’ Level Additional Mathematics (revision)

* other syllabuses that involve geometry and coordinate geometry / analytic geometry
* whoever is interested