Olympiad 3
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2. cos A + cos B + cos C = 4 sin A 2 sin B 2 sin C 2<br />
3. tan A + tan B + tan C = tan A tan B tan C<br />
4. tan A 2 tan B 2 + tan A 2 tan C 2 + tan B 2 tan C 2 = 1<br />
Exercise 22. ABCD is a quadrilateral<br />
whose diagonals intersect at O.<br />
If ∠AOB = 30 ◦ , AC = 24 cm and<br />
BD = 22 cm, find the area of ABCD.<br />
B<br />
A<br />
30 ◦<br />
O<br />
D<br />
C<br />
Exercise 23. In the figure, ABCDEF is a regular hexagon with area equal<br />
to 3 √ 3 cm 2 . Find the area of the square P QRS.<br />
Q<br />
C<br />
B<br />
P<br />
D<br />
A<br />
R<br />
E<br />
F<br />
S<br />
Exercise 24. ABCD is a square,<br />
AEF is a n isosceles triangle, and<br />
∠EAF = 30 ◦ . Points E and F lie on<br />
BC and CD respectively. The area of<br />
△AEF is 1. Find the area of ABCD.<br />
D<br />
30 ◦<br />
F<br />
C<br />
E<br />
A<br />
B<br />
Exercise 25. The perimeters of an equilateral triangle and a regular hexagon<br />
are equal. If the area of the triangle is 5 square units. Find the area of the<br />
hexagon in square units.<br />
6 Score:
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