Question

Точка О является центром окружности радиусом 7дм. АО=6дм, ВО=8дм, CD=15дм.Внутри или вне окружности лежит точка А? Точка В? Могут ли обе точки C иD лежать внутри окружности? Вне окружности?

Answer 1

Точка А лежит внутри окружности, т.к. ОА=6 дм< радиуса=7 дм
Точка В лежит вне окружности, т.к. ОВ=8 дм> радиуса=7 дм
 Внутри окружности может лежать только одна из точек С или D. Они обе могут лежать вне окружности.

Answer 2

Question Analysis

The question asks about the positions of points A, B, C, and D in relation to a circle with a radius of 7 dm. The distances AO, BO, CD are also given. We need to determine whether points A and B are inside or outside the circle, and whether points C and D can both be inside the circle.

Answer

To determine the positions of points A, B, C, and D in relation to the circle, we can use the following information: - The radius of the circle is 7 dm. - The distance AO is 6 dm. - The distance BO is 8 dm. - The distance CD is 15 dm.

Position of Point A

To determine whether point A is inside or outside the circle, we need to compare the distance AO with the radius of the circle. If AO is less than the radius, point A is inside the circle. If AO is equal to the radius, point A is on the circle. If AO is greater than the radius, point A is outside the circle.

Given that AO is 6 dm and the radius of the circle is 7 dm, we can conclude that point A is inside the circle because AO is less than the radius. Point A is inside the circle.

Position of Point B

Similarly, to determine whether point B is inside or outside the circle, we need to compare the distance BO with the radius of the circle. If BO is less than the radius, point B is inside the circle. If BO is equal to the radius, point B is on the circle. If BO is greater than the radius, point B is outside the circle.

Given that BO is 8 dm and the radius of the circle is 7 dm, we can conclude that point B is outside the circle because BO is greater than the radius. Point B is outside the circle.

Positions of Points C and D

To determine whether both points C and D can be inside the circle, we need to consider the distances CD and the radius of the circle. If both CD and the sum of the distances from the center of the circle to points C and D are less than the radius, then both points C and D can be inside the circle. Otherwise, if either CD or the sum of the distances from the center of the circle to points C and D is greater than or equal to the radius, then at least one of the points C and D is outside the circle.

Given that CD is 15 dm and the radius of the circle is 7 dm, we can conclude that at least one of the points C and D is outside the circle because CD is greater than the radius. Both points C and D cannot be inside the circle.

Summary

In summary: - Point A is inside the circle. - Point B is outside the circle. - Both points C and D cannot be inside the circle.

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