Geometry concept session 4

1. Alosies George
IIM Calcutta
director@georgeprep.com
+91- 9985-372-371
www.georgeprep.com
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Geometry Concept Session 4

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Circles

3. Terminology
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4. Terminology
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5. Properties
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Equal arcs subtend equal angels at the
centre of the circle.
If two arcs subtend equal angles at the
centre of the circle, then the arcs are
equal.
l = rθ

6. Properties
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Equal chords subtend equal angles at
the centre of the circle.
Equal angles subtended at the centre of
the circle cut off equal chords.

7. Properties
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A perpendicular line from the centre of a
circle to a chord bisects the chord.
A line from the centre of a circle that
bisects a chord is perpendicular to the
chord.

8. Properties
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Equal chords are equidistant from the
centre of the circle.
Chords that are equidistant from the
centre are equal.

9. Problems
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CAT 2003 (L)
Answer: Option 1

10. Properties
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Intersection : Internal
The products of intercepts of
intersecting chords are equal
AX.XB = CX.XD

11. Properties
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Intersection : External
The square of the length of the tangent
from an external point is equal to the
product of the intercepts of the secant
passing through this point.
(AX)2 = BX.CX

12. Properties
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The angle at the centre of a circle is
twice the angle at the circumference
subtended by the same arc

13. Properties
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Angle in a semicircle is a right angle.

14. Properties
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Angles standing on the same arc are
equal.

15. Properties
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Tangents to a circle from an exterior
point are equal.

16. Properties
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When two circles touch, the line through
their centres passes through their point
of contact.

17. Properties – Alternate segment theorem
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The angle between a tangent and a
chord through the point of contact is
equal to the angle in the alternate
segment.

18. Problems
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CAT 2008
Answer: Option 5

19. Problems
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CAT 2003 (L)
Answer: Option 3

20. Problems
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CAT 2005
Answer: Option 1