Question

Задачі. 7. Сторони кута перетинають паралельні прямі AA, і BB1 так, що ОА =А В. Знайдіть ОВь, якщо А10= 14см 8. Навколо трикутника ABC описано коло. Знайдіть градусні міри дуг AB, BC i AC, якщо LA = 30º, LB = 62°. 9. Три сторони трапеції, взятi послідовно, відносяться як 3 : 4 : 9. Знайдіть сторони трапеції, якщо її периметр дорівнює 60см.​

Answer 1

Task 7: Finding the Length of OV

To find the length of OV in the given diagram where sides of an angle intersect parallel lines AA and BB1 such that OA = A B and A10 = 14 cm.

The length of OV can be found using the given information. Let's calculate it.

Solution: Using the given information, we can calculate the length of OV using the following steps:

1. Since OA = A B, it implies that triangle OAB is an isosceles triangle. 2. By the property of isosceles triangles, the perpendicular bisector of the base of the triangle passes through the vertex. 3. Therefore, OV is the perpendicular bisector of AB, and it divides AB into two equal parts. 4. Hence, OV = 1/2 * AB.

Given A10 = 14 cm, we can calculate the length of OV.

Calculation: OV = 1/2 * AB OV = 1/2 * A10 OV = 1/2 * 14 cm OV = 7 cm

So, the length of OV is 7 cm.

Task 8: Finding the Angles of the Inscribed Circle

In the given scenario where a circle is inscribed around triangle ABC and the angles LA = 30º and LB = 62°, we need to find the degree measures of the arcs AB, BC, and AC.

The degree measures of the arcs can be calculated using the given angle measures.

Solution: To find the degree measures of the arcs AB, BC, and AC, we can use the following steps:

1. The degree measure of an arc is twice the degree measure of the angle subtended by the arc at the center of the circle. 2. Therefore, the degree measure of arc AB = 2 * LA and the degree measure of arc BC = 2 * LB.

Calculation: Degree measure of arc AB = 2 * LA = 2 * 30º = 60º Degree measure of arc BC = 2 * LB = 2 * 62° = 124° Degree measure of arc AC = 360º - (Degree measure of arc AB + Degree measure of arc BC) Degree measure of arc AC = 360º - (60º + 124°) Degree measure of arc AC = 360º - 184° Degree measure of arc AC = 176°

So, the degree measures of the arcs AB, BC, and AC are 60º, 124°, and 176° respectively.

Task 9: Finding the Sides of a Trapezium

In the given problem where the sides of a trapezium are in the ratio 3:4:9 and the perimeter is 60 cm, we need to find the lengths of the sides of the trapezium.

The lengths of the sides can be calculated using the given ratio and perimeter.

Solution: To find the lengths of the sides of the trapezium, we can use the following steps:

1. Let the sides of the trapezium be 3x, 4x, and 9x, where x is a common multiplier. 2. The perimeter of the trapezium is the sum of all its sides, which is given as 60 cm. 3. Therefore, 3x + 4x + 9x = 60 16x = 60 x = 60 / 16 x = 3.75

Now, we can find the lengths of the sides by substituting the value of x.

Calculation: Length of the first side = 3x = 3 * 3.75 = 11.25 cm Length of the second side = 4x = 4 * 3.75 = 15 cm Length of the third side = 9x = 9 * 3.75 = 33.75 cm

So, the lengths of the sides of the trapezium are 11.25 cm, 15 cm, and 33.75 cm respectively.