Question

Question:
8 points lie on the circumference of a circle. How many more quadrilaterals can be formed by connecting these points compared to the number of triangles?

Options:
(1) 14
(2) 24
(3) 16
(4) 18

Answer 1

To solve this problem, let's break it down step-by-step:

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Step 1: Calculate the Number of Triangles

To form a triangle, we need to select 3 points out of the 8 points on the circumference. The total number of triangles is given by the combination formula:

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Step 2: Calculate the Number of Quadrilaterals

To form a quadrilateral, we need to select 4 points out of the 8 points on the circumference. The total number of quadrilaterals is:

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Step 3: Difference Between Quadrilaterals and Triangles

Now, we calculate the difference between the number of quadrilaterals and triangles:

Difference=70−56=14

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Final Answer:

(1) 14