📐 geometry

1. **State the problem:** We are given a circle with points A, B, D on a vertical line and a radius labeled $a$. Segments $AD=12$ and $AB=10$ are given. We want to find the equatio

1. **State the problem:** We need to find the area of the shaded segment in a circle with radius 12 cm and central angle 47°. 2. **Recall the formula:** The area of the segment is

1. **Problem statement:** Find the area of the shaded triangle inside a circle with radius 12 cm and central angle 47°. 2. **Formula for the area of a triangle with two sides and i

1. The problem involves two separate geometric setups with unknown $x$ values to solve for. 2. First problem: A triangle with a circle inside it, where one side is 14, a segment ad

1. The problem is to create a geometry paper for 10th grade English medium SSC, similar to SSC format. 2. Since this is a request for a paper format, not a specific math problem, w

1. **Problem statement:** We have a circle with points P, Q, R on the circumference and secants PS and RT intersecting outside the circle. Given segment lengths: $PT=2.4$, $PQ=7$,

1. The problem is to find a certain value or relationship using 2 triangles. 2. When using two triangles, common methods include comparing corresponding sides or angles, using simi

1. **State the problem:** We need to find the area of a circle with radius $r = 3$ cm. 2. **Formula for the area of a circle:** The area $A$ is given by the formula

1. **State the problem:** We need to find the area of a circle with radius 18 ft in terms of $\pi$. 2. **Formula:** The area $A$ of a circle is given by the formula:

1. Problem 14 to 30 includes multiple distinct questions, but per instructions, we solve only the first one, which is 25.a: Find the coordinates of M and draw the rectangle. 2. Giv

1. The problem is to find the length of the third side of a right triangle where the two legs are given as $7$ and $\sqrt{51}$.\n2. We use the Pythagorean theorem for right triangl

1. **State the problem:** We have a right triangle with two legs each of length 8, and we need to find the length of the third side (the hypotenuse). 2. **Formula used:** The Pytha

1. **Problem Statement:** Find the length of the zip line AD in a rectangular prism where the zip line runs diagonally from corner A to opposite corner D, making a 60° angle with p

1. **Problem Statement:** Determine the shortest path from Start to Finish on the obstacle course given three possible routes: - A. Start to A to D to Finish

1. **State the problem:** We need to determine whether the distance between the tips of the clock hands is greater at 4:00 or 7:00 using the Hinge Theorem. 2. **Recall the Hinge Th

1. **State the problem:** We have a right triangle with one leg measuring 12 cm, the hypotenuse measuring 39 cm, and the other leg labeled as $x$ cm. We need to find the length of

1. **Problem Statement:** Given two parallel lines $p$ and $f$ intersected by a transversal $t$, we observe angles formed at the intersections. We need to find the value of $x$ in

1. **State the problem:** We have a right triangle with angles 30\degree, 60\degree, and 90\degree. The side adjacent to the 30\degree angle is $3 - \sqrt{6}$ miles, and the side o

1. **State the problem:** We have a right triangle with angles 30°, 60°, and 90°. The side adjacent to the 30° angle is $3 - \sqrt{6}$ miles, and the side opposite the 30° angle is

1. **State the problem:** We need to find the area of a parallelogram with a base of 15 cm and a height of 8 cm. 2. **Formula:** The area $A$ of a parallelogram is given by the for

1. The problem is to find the area of a trapezoid with the top base $2$ m, bottom base $6$ m, and height $4$ m. 2. The formula for the area $A$ of a trapezoid is: