Triangle Question 5 || 9&10 Math Capsule || Misbah Sir || Infinity Learn Class 9&10

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.

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

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.

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 one-third of AD, so it can be determined by multiplying the length of AD by two-thirds. 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.