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Introduction to geometrical properties of circle
In the following two videos, the geometrical properties of a circle are being discussed in the following sequence (Take note that these are the short forms of the geometrical properties of a circle and these reasons must be given when you attempt questions on circles):
1. tan ⊥rad
2. ∠ at centre = 2 ∠ at circumference
3. ∠s in same segment
4. ∠ in semicircle
5. ∠s in opp. segments OR opp. ∠s in cyclic quad.
6. ∠s in alt. segments OR alt. segment theorem
7. tangents from an external point
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1. tan ⊥rad
2. ∠ at centre = 2 ∠ at circumference
3. ∠s in same segment
4. ∠ in semicircle
5. ∠s in opp. segments OR opp. ∠s in cyclic quad.
6. ∠s in alt. segments OR alt. segment theorem
7. tangents from an external point
CLICK HERE TO VIEW FIRST VIDEO
CLICK HERE TO VIEW SECOND VIDEO
Solving questions on geometrical properties of circles (part 1)
Take note that the following three parts of the video clips do not show the complete presentation of solution including the writing of reasons for finding angles. For the complete presentation of solutions to geometrical properties of circles, please consult your school teachers.
However, the video clips provide the thinking process to solve the questions. The idea here is to be open-minded and very observant by breaking the whole circle diagram into smaller parts to look at in order to see the application of the geometrical properties to various smaller parts in the circle. The more questions one practise, the more experienced and faster the thinking process to seeing the circle in various smaller parts to apply the geometrical properties.
However, the video clips provide the thinking process to solve the questions. The idea here is to be open-minded and very observant by breaking the whole circle diagram into smaller parts to look at in order to see the application of the geometrical properties to various smaller parts in the circle. The more questions one practise, the more experienced and faster the thinking process to seeing the circle in various smaller parts to apply the geometrical properties.
Solving questions on geometrical properties of circle (part 2)
Solving questions on geometrical properties of circle (part 3)
Please ignore the first 2 minutes of this video. Start viewing from the time 2 minutes onwards for the discussion of a fresh question.