Triangle Question 5  9&10 Math Capsule  Misbah Sir  Infinity Learn Class 9&10  Summary and Q&A
TL;DR
The video demonstrates how to find the length of GD in a triangle using the Apollonius theorem, with a final answer of 92.
Key Insights
 🔨 The Apollonius theorem is a useful tool in solving problems related to triangles.
 🗂️ The midpoint of a side in a triangle divides it into two equal segments.
 🥳 The centroid of a triangle divides each median into segments with a ratio of 2:1.
 💁 It is important to carefully apply the given information and formulas to solve geometry problems accurately.
 The length of GD in the given triangle is equal to 2/3 times the square root of 86.
 😊 The value of a + b + d + 1 in the problem equals 92.
 🔺 The Apollonius theorem can be used to find missing lengths or solve for unknown variables in a triangle.
Transcript
so let's first make this figure according to the given question let's make the triangle in verb so that is a b and c we want to find the length of GD so for that I have to join this median this will be a median guys because these the midpoint of BC in order to find the length of a d we can use the a Polonius theorem right if you simplify this equat... Read More
Questions & Answers
Q: What is the Apollonius theorem, and how is it used in this problem?
The Apollonius theorem states that 2 times AD^2 plus BD^2 equals AB^2 plus AC^2. In this problem, it is used to find the length of GD by substituting the known values for AB, AC, and BD.
Q: How is the value of AD^2 determined?
By applying the Apollonius theorem and simplifying the equation, AD^2 is found to be equal to 344.
Q: What is the length of AD?
The length of AD is equal to the square root of 344, which simplifies to 2√86.
Q: How is the length of GD determined?
GD is onethird of AD, so it can be determined by multiplying the length of AD by twothirds. Therefore, the length of GD is 2/3 times the square root of 86.
Summary & Key Takeaways

The video discusses how to find the length of GD in a triangle ABC, where D is the midpoint of BC and G is the centroid of the triangle.

The Apollonius theorem is used to solve the problem, which states that 2 times AD^2 plus BD^2 is equal to AB^2 plus AC^2.

By applying the Apollonius theorem and simplifying the equation, the length of GD is found to be 2√86.