The image shows a mathematical problem, likely related to geometry, and a diagram of a circle with six points labeled A, B, C, D, E, and F along its circumference. The text is written in Indonesian and appears to ask how many triangles can be formed if three points are chosen from these six points on the circle.

Problem Interpretation:

Translation: There are 6 points on the circumference of a circle, as shown in the image. If 3 of these 6 points are connected to form a triangle, how many distinct triangles can be formed?

Solution:

To solve this, we need to determine how many ways we can choose 3 points out of the 6 points to form a triangle. This is a combination problem, and the formula for combinations is given by:

$\binom{n}{r} = \frac{n!}{r!(n-r)!}$

Where:

• $n$ is the total number of points (6 in this case),
• $r$ is the number of points to choose (3 in this case).

Substituting the values:

$\binom{6}{3} = \frac{6!}{3!(6-3)!} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20$

Final Answer:

Therefore, 20 distinct triangles can be formed by selecting 3 points out of 6 on the circle.

Would you like further details or have any questions?

Follow-up questions:

1. How would the number of triangles change if there were 7 points on the circle?
2. What if the points were arranged in a different shape rather than a circle—would the solution still apply?
3. Can you derive the combination formula for selecting 3 points from any number of points?
4. What happens if two or more points are collinear? Would that affect the number of triangles formed?
5. How many quadrilaterals can be formed from 6 points on the circumference of the circle?

Tip: The combination formula is useful not only for counting triangles but also for many other situations where you need to select a subset from a larger group.