📘 geometry, algebra

1. সমস্যাটি হলো: A(-1,3) এবং B(2,5) পয়েন্টের মধ্যে AB রেখার দৈর্ঘ্য নির্ণয় করা। 2. AB রেখার দৈর্ঘ্য নির্ণয়ের সূত্র হলো: $$AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ যেখানে $A(x

1. **Problem Statement:** (a) Points $P(x_1,y_1)$, $Q(x_2,y_2)$, and $R(x,y)$ lie on a circle with $PQ$ as the diameter. Show the equation of the circle.

1. Problem 4: Find the direct distance from home to work given a right triangle with legs 12 mi east and 9 mi north. 2. Use the Pythagorean theorem for right triangles: $$c = \sqrt

1. **Problem 8a:** Find the number of sides of a regular polygon with an internal angle of 150°. The formula for the internal angle $I$ of a regular polygon with $n$ sides is:

1. **Problem:** A diagonal of a rectangle is inclined to one side at 25°. Find the acute angle between the diagonals. 2. **Formula:** In a rectangle, diagonals are equal and bisect

1. **حل المعادلات المعطاة:** أ) المعادلة $x^2 - y^2 + 2x + 4y - 15 = 0$

1. Problem 12: We need to build a wall 100 feet long and 7 feet high using 1-foot-high blocks that are either 1 or 2 feet long. The vertical joints must be staggered, and the wall

1. **Problem 31:** The difference between the outer and inner radii of a hollow right circular cylinder of length 14 cm is 1 cm. The volume of the metal used is 176 cm³. Find the o

1. **Triangle problem:** Given a right triangle with base segments 7.3 cm and 2.7 cm, the vertical side opposite angle $\theta$ is $7.3 - 2.7 = 4.6$ cm, and the total base is $7.3

1. **Problem statement:** Calculate various geometric and trigonometric properties of the tent roof and complete a table for the cubic function. ### Question 19

1. **Problem 22:** Given triangle ABC with sides AB = 6, AC = 8, BC = 12, point P lies on AB such that AP = 4, and Q lies on AC so that \(\angle APQ = \angle ACB\). Find length PQ.

1. The problem states that the two shapes have equal areas. We are asked to find the ratio $k : m$. 2. The left shape is a right-angled triangle with base $k$ cm and height 12 cm.

1. **(A) Area of triangle using base and altitude:** The area of a triangle is given by the formula: