Higher MathFundamental ConceptNCTB উচ্চতর গণিত অধ্যায় ৩ (জ্যামিতি)
Apollonius Theorem
Bengali: অ্যাপোলোনিয়াসের উপপাদ্য•Pronunciation: অ্যাপোলোনিয়াস থিওরেম•Symbol: 3\sum a^2 = 4\sum d^2
Standard Definition:
A theorem relating the length of a median of a triangle to the lengths of its three sides.
📐 Mathematical Equation, Units & Dimensions
Defining Mathematical Equation
Standard SI Unit
Geometric area ratio(জ্যামিতিক ক্ষেত্রফল অনুপাত)
Dimensional Analysis
CGS Unit
None
📖 Physical Concept & Comprehensive Explanation
Generalizes the Pythagorean theorem to arbitrary triangles, relating median lengths to side lengths as AB^2 + AC^2 = 2*(AD^2 + BD^2). It yields the universal median identity: 3 * sum(sides^2) = 4 * sum(medians^2).
🎯 High-Yield Revision Points
- ✓Equation: AB^2 + AC^2 = 2(AD^2 + BD^2).
- ✓Used to compute median lengths directly from side dimensions.
- ✓Proves 3 * sum(sides^2) = 4 * sum(medians^2).
Use Online Solver for Apollonius Theorem
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❓ Frequently Asked Exam Questions (FAQ)
Common questions in board and competitive entrance examinations
Q1: State Apollonius' Theorem.
The sum of the squares on any two sides of a triangle equals twice the square on half the third side plus twice the square on the median bisecting the third side.