Rotate an equilateral triangle inscribed in a circle 40 degrees clockwise and counterclockwise, as shown in the figure below. How many triangles are there in the figure?

Fill in the circles with the numbers 1, 2, 3, 4, 5, 6 and 7. Each number can be used once without repetitions. The sum of the digits inside the circles at the four vertices of the square on the left is 15 and the sum of the digits inside the circles at the vertices of the regular pentagon on the right is 24. How many possible arrangements are there?

An ant is clinging to one corner of a box in the shape of a cube. The ant wants to get to the most distant corner of the box by crawling only along the edges of the cube and without ever revisiting a place it has been. How many different paths can the ant take to the most distant corner?

Point B,DB,D and JJ are midpoints of the sides of right triangle ACGACG . Points K,E,IK,E,I are midpoints of the sides of triangle JDGJDG, etc. If the dividing and shading process is done 100 times (the first three are shown) and AC=CG=6AC=CG=6, then the total area of the shaded triangles is nearest

ABCD,CEFGABCD,CEFG and DGMNDGMN are squares, with GG on CDCD and FF on MGMG. If AB=10cmAB=10cm and MN=6cmMN=6cm, what is the area of triangle AMEAME, in cm2cm2?

In a right-angled △ABC,∠A=900,AD⊥BC,D△ABC,∠A=900,AD⊥BC,D is a point on BCBC. If BD=3.6,AC=8BD=3.6,AC=8. Find the area of △ACD△ACD

In the 6 × 8 square grid, the area of each square is 1 cm2, what is the shaded area, in cm2?

1 How many triples of integers (a,b,c) are there such that
?

2

ABC and RTS are similar triangles.
The value of x is

In a right-angled △ABC,∠A=900,AD⊥BC,D△ABC,∠A=900,AD⊥BC,D is a point on BCBC. If BD=3.6,AC=8BD=3.6,AC=8. Find the area of △ACD△ACD