📐 geometry

1. **State the problem:** We are given that the ratio of one side of triangle ABC to the corresponding side of triangle DEF is $5:8$, and the perimeter of triangle DEF is 96 inches

1. **State the problem:** We need to find the area of a walkway formed by four semicircles. The inner semicircles have a diameter of 14 metres, and the walkway width between the in

1. **Problem statement:** We need to find the side length of the smallest square plate on which a 22-cm chopstick can fit along the diagonal without any overhang. 2. **Formula used

1. **Problem Statement:** Prove the SAS (Side-Angle-Side) congruence theorem which states that if two sides and the included angle of one triangle are equal to two sides and the in

1. **Problem statement:** Given pentagon ABCDE with circle center O passing through A, C, D, E, angles $\angle EAC=36^\circ$, $\angle CAB=78^\circ$, and $AB \parallel DC$. Find $x,

1. **State the problem:** Prove that two triangles are congruent if two sides and the included angle are the same. 2. **Recall the SAS Congruence Theorem:** If two sides and the in

1. **Problem statement:** Given pentagon ABCDE with circle center O passing through A, C, D, E, angles $\angle EAC=36^\circ$, $\angle CAB=78^\circ$, and $AB \parallel DC$. Find $x$

1. ප්‍රශ්නය: වෘත්තයක් තුළ U මධ්‍යස්ථානය වන අතර P, Q, R, S, T, U, V යන ලක්ෂ්‍ය සහ PS, PR, QR, QT, TR, UT යන රේඛා කොටස් ඇත. QT = TR සහ QTU = UTR යන සමානතා දී ඇත. S Q V + U V R = S P

1. Problem statement. In the cyclic pentagon ABCDE the points A, C, D and E lie on a circle with centre O, AB is parallel to DC, $\angle EAC = 36^\circ$ and $\angle CAB = 78^\circ$

1. **Problem statement:** Calculate the area of the rectangle with given dimensions 6 m (top line) and 4 cm (right line) using the scale 1 : 40,000. 2. **Understanding the scale:**

1. **State the problem:** We have a circle with points A, B, C, D on the circumference and a tangent EBF at point B. Given angles are $\angle BAC = 40^\circ$ and the angle between

1. **State the problem:** We have a circle with radius $14$ cm and two chords $AB$ and $CD$ with lengths $12$ cm and $10$ cm respectively. We need to find the distance of each chor

1. **Problem statement:** We have a circle with center $O$ and points $A$, $B$, $C$, and $D$ on its circumference. A tangent line $FDE$ touches the circle at point $D$. We need to

1. **State the problem:** We need to find the size of angle $\angle DAC$ in a circle with diameter $AC$, where $\angle CAB = 25^\circ$ and $\angle DEC = 100^\circ$. 2. **Recall key

1. **State the problem:** We have points A, B, C, D on a circle, with C, D, E collinear. Given that $BA = BD$, $CB = CD$, and angle $ABD = 40^\circ$, we need to find the size of an

1. **Problem statement:** We have triangle RUZ with sides $RU=47$ cm, $RZ=102$ cm, and angle $Z=23^\circ$. We need to find the measure of the obtuse angle $RUZ$ (angle at $U$). 2.

1. **Problem statement:** We have two parallel lines $a$ and $b$ with a 45° right triangle placed between them. Given that angle $\angle 1 = 15^\circ$, we need to find the size of

1. **Problem Statement:** Use the Pythagorean theorem to find the length of the hypotenuse $c$ in a right triangle with legs $a$ and $b$. 2. **Formula:** The Pythagorean theorem st

1. **Stating the problem:** We have a geometric figure with angles 45°, 80°, and unknown angles $a^\circ$, $b^\circ$, $c^\circ$, and $d^\circ$. We need to find the values of $a$, $

1. **State the problem:** Calculate the perimeter and area of the given irregular "T"-shaped polygon with dimensions 10 cm and 4 cm. 2. **Perimeter calculation:** The perimeter is

1. **State the problem:** We have a cuboid with length $L$ cm, width $W$ cm, and height $H$ cm. The net of the cuboid shows dimensions: total horizontal length $37.8$ cm and vertic