angle properties of circle

A-Maths: Find Equation of Circle Given Tangent & Circle + More

Many students after reading the question take a long time to begin as they don't know how to start. The trick is to draw! Drawing helps us to see and understand the question better.

Drawing is one of the keys to answer this question. To answer part (a), we need to notice the property of radius is perpendicular to tangent. Also, in part (b) of the question, we need to apply discriminant from the topic of Quadratic.

I have shared my thinking process and step-by-step solutions in the following videos.

How did you find the videos? Did they help you to understand better? Leave me your feedback in the comment section.

Part (a) URL: Click here to watch part (a) 7 minutes

Part (b) & (c) URL: Click here to watch part (b) & (c) 5 minutes.

A-Maths: Plane Geometry Question (Step-by-Step) [Video]

In this video, I will show you:

How to prove that 2 lines are // to each other
How to prove a pair of similar triangles
How to prove an equation involving length

Properties & Theorems used:

Angles in the same segment
Intercept Theorem
Corresponding angles
Tangent - Secant Theorem

Strategies (Used in manipulation in part iii) :

Breaking a longer length into smaller parts
'Expansion' of length
Using result from earlier parts
Factorising common length

If you find this video, please subscribe to my YouTube Channel and share it with your friends!

Link to video: http://www.youtube.com/watch?v=UNZolJverww

Thank you!

Length of video = 11 minutes.

E-Maths: Introduction of Angle Properties of Circle (Basic) - Video

This topic, Angle Properties of Circle is usually introduced in Secondary 3 Elementary Maths syllabus in Singapore. It is a very visual topic in which some students might have challenges "seeing" and "identifying" them.

I would like to first introduce the 5 Angle Properties of Circle:

Angles in the same segment (are equal)
Angle at centre is twice angle at the circumference
Right angle in semi-circle
Angles in opposite segment (add up to 180 degrees)
Radius is perpendicular to tangent

I have shared these 5 Angle Properties of Circle in the following video.

Direct link: https://www.youtube.com/watch?v=xrI8jpOny2Y

For those of you who have challenges with this topic, tell me what are the challenges you face in the comment section below.

E-Maths: Angle Properties of Circle Question

In this video, I discuss on the methods to answer angle properties of circle.

2 items to mark out before answering the question.
How to identify angle at centre and its angle at circumference.
Common perception mistake on cyclic quadrilateral.

Length of video = 6.35 minutes.

Download the question in pdf here.

Direct link to video, click here.

Video Solution Of Plane Geometry Question (Plus:Strategy To Handle Angles)

This is the step by step video solution for this Plane Geometry question

Inside this video, you will get to know how I begin this question with a clear objective and the steps I took to achieve this objective.

I used 2 strategies (on differentiating the angles) to quickly and easily prove this question.

Letting an angle be x
Usage of color (In exams, you can perhaps use different type of lines to differentiate the angles as well)

Hear from you on this approach. If you have your own approach, we would love to hear from you.

Leave me a comment in the section below.