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| Geometry
- Plane Figures Problems and Solutions |
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Plane figures, solved problems, examples |
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| Example:
The ratio of the area of the circumcircle and the area of the inscribed regular dodecagon is? |
| Solution: Given
n
= 12. A
circle
: A12
= ? |
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| Example:
In a circle the chord
AB subtends the central angle
a
and the chord
CD
subtends the central angle b, if given are,
d(AB) =
a and angles
a
and
b, then
d(CD)
is? |
| Solution: Given
d(AB) =
a,
a and
b.
d(CD)
= ? |
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| Example:
The area of the sector
A = 64 and the perimeter
P
= 32, find the length of its arc. |
| Solution: Given A = 64 and
P
= 32. arc
l
= ? |
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| Example:
Bases of an isosceles trapezium are,
21 cm and
9 cm, and its height
8 cm. The radius of its circumcircle is? |
| Solution: Given
a
= 21 cm,
c
= 9 cm and
h
= 8 cm.
r
= ? |
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| Example:
Find the area of the intersection of two circles with the same radius
r = 8 whose centers lay on each other
circumferences. |
| Solution: Given r = 8.
A
intersection
= ? |
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| Example:
The area of an annulus equals the quarter of the area of the inner circle. The ratio of the radius of the inner circle
to the radius of the outer circle is? |
| Solution: Given
Aanulus
= 1/4 ·
Ar2.
r2
: r1
= ? |
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| Example:
The ratio of the radius of the incircle to the radius of the circumcircle of a right triangle with legs, a = 3 and
b
= 4, is? |
| Solution: Given a = 3 and
b
= 4. r
: R
= ? |
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| Geometry
and use of trigonometry contents - A |
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| Copyright
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