Step-by-Step Breakdown
The circle is divided by straight lines originating from the center point. We can clearly observe:
-
4 lines radiating from the center, dividing the circle into 8 equal triangular slices.
-
A horizontal line and a vertical line intersecting through the center.
-
Two diagonal lines intersecting through the center, forming a star-like shape.
Now, let’s identify and count the different types of triangles.
1. Basic Triangles from the Center
Each of the 8 segments (or “pizza slices”) forms a basic triangle. These are the most obvious shapes.
Count so far: 8 triangles
2. Combinations of Adjacent Triangles
Now, consider the possibility of combining two adjacent slices into larger triangles. If you combine two neighboring triangles, you get a triangle that spans two of the original slices.
There are 8 of these combinations:
-
(1+2), (2+3), …, (8+1) – total of 8 new triangles.
Count so far: 8 (original) + 8 (combinations) = 16 triangles
3. Larger Triangles from Diagonal Intersections
If you look closely at the diagonal and horizontal/vertical divisions, you’ll notice that combining non-adjacent segments and lines can form larger triangles that span a quarter or half of the circle.
Each quadrant of the circle contains 2 smaller triangles that, when combined, can form:
-
One larger triangle per quadrant.
There are 4 quadrants, so:
4 more large triangles.
Count so far: 16 + 4 = 20 triangles
4. Hidden or Overlapping Triangles
When diagonal and vertical/horizontal lines intersect within each segment, especially near the center, additional smaller triangles are formed inside what were originally seen as single segments. Each triangular section may be split into 2 smaller triangles, depending on the specific geometry of how the lines intersect.
Upon closer inspection, you can find:
-
2 small triangles per segment × 8 segments = 16 small inner triangles
Count so far: 20 + 16 = 36 triangles
Final Answer: 36 Triangles
Why This Puzzle Is So Tricky
The reason this puzzle stumps so many people is that the brain tends to focus on the most obvious, large shapes and often overlooks how lines inside a shape can subdivide it further. Additionally, our eyes naturally assume symmetry and simplicity, but the challenge lies in spotting composite and overlapping figures—especially near the center where the lines converge tightly.
This image teaches us not just about geometry, but also about perception. It’s a fun reminder that sometimes, looking a little deeper reveals much more than first meets the eye.
So the next time someone asks you how many triangles are in the picture, you can confidently say: 36.
