12 Class Math Exercise 6.3 Complete || 2nd Year Mathematics Exercise 6.3 Complete

12 Class Math Exercise 6.3 Complete || 2nd Year Mathematics Exercise 6.3 Complete

Circle Theorems | Normal, Tangent, Circumcentre, Mean Proportional | Intermediate Part 2 Math

12 Class Math Exercise 6.3 Question No.1
12 Class Math Exercise 6.3 Question No.2
12 Class Math Exercise 6.3 Question No.3
12 Class Math Exercise 6.3 Question No.4

In this video, we'll prove four important theorems related to circles:

1. Normal Line Passes Through Centre of The Circle
2. Line Perpendicular to Tangent Passes Through Point of Tangency
3. Midpoint of Hypotenuse of Right Triangle is Circumcentre
4. Perpendicular from Any Point of Circle to Diameter is Mean Proportional

We'll solve examples from Ex. 6.3, questions 1-4, of Punjab, KPK, and Federal Board Intermediate Part 2 Mathematics.

_Normal Line Passes Through Centre of The Circle_

- Proof: Using the equation of a normal line and the centre of the circle
- Examples: Finding the equation of a normal line and verifying it passes through the centre

_Line Perpendicular to Tangent Passes Through Point of Tangency_

- Proof: Using the equation of a tangent line and the point of tangency
- Examples: Finding the equation of a line perpendicular to a tangent and verifying it passes through the point of tangency

_Midpoint of Hypotenuse of Right Triangle is Circumcentre_

- Proof: Using the midpoint formula and the circumcentre of a triangle
- Examples: Finding the circumcentre of a right triangle and verifying it's the midpoint of the hypotenuse

_Perpendicular from Any Point of Circle to Diameter is Mean Proportional_

- Proof: Using the equation of a circle and the diameter
- Examples: Finding the mean proportional and verifying it's equal to the perpendicular distance

_Examples & Solutions_

- Solving questions 1-4 from Ex. 6.3, Punjab, KPK, and Federal Board Intermediate Part 2 Mathematics
- Step-by-step solutions and explanations

_Conclusion_

In conclusion, we've proved four important theorems related to circles. We hope this video has helped you master these concepts and equations.

_Hashtags:_
#pw #PhysicsWallah #12ClassMath #IntermediateMath #ConicSections #Circle #Theorems #Normal #Tangent #Circumcentre #MeanProportional #Mathematics #Part2 #Intermediatemath #PunjabBoard #KPKBoard #FederalBoard #Maths #Mathematics #Class12 #InterMediate #Mathematics #CircleTheorems #MathExamples #MathTutorials #MathLessons #MathConcepts #MathProblems #MathSolutions #MathGraphs #MathTables #MathFormulas #MathEquations #MathAlgebra #MathGeometry #MathCalculus #MathStatistics #MathTrigonometry #MathCoaching #MathTutoring #MathStudyTips #MathExamPrep