Let A1, A2, A3, A4,........, A8 be the vertices of the regular octagons that lie on the circle of radius 2. Let p be a point on the circle and let PAi denote the distance between the point P and Ai for i = 1,2,3,....,8. If P varies over the circle, then the maximum value of the product is PA1.Pa2..........PA8, is
Correct Answer: 512
Solution and Explanation
The correct answer is: 29 = 512
The vertices A1, A2, A3, ..., A8 of a regular octagon are positioned on a circle with a radius of 2. Consider Z as the result of evaluating (2) × (1) × (1/8), resulting in Z8 being equal to 28 × 1.
Thus, the expression Z8 – 28 equals zero.MAX ( P1,P2,P8)=29 = 512
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Concepts Used:
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Let's consider line ‘L’ is passing through the three-dimensional plane. Now, x,y, and z are the axes of the plane, and α,β, and γ are the three angles the line making with these axes. These are called the plane's direction angles. So, correspondingly, we can very well say that cosα, cosβ, and cosγ are the direction cosines of the given line L.
Read More: Introduction to Three-Dimensional Geometry