Geometry Answers

Line 1 touches the circle ω at point K. Points A and B are chosen on ω in such a way that they are situated on opposite sides with respect to the diameter of ω that passes through point K. Find the area of triangle AKB if the distances from points A and B to line 1 are equal to 7 and 11 respectively, and AK=13. Round the answer to the closest integer.

Let AK, BL, CN be angle bisectors of triangle ABC, and they intersect at point I. It is known that the ratios of areas of triangles BKN and CLK to the area of triangle ABC are equal to \frac{1}{10} and\frac{16}{25} respectively, and ratio IK:AI is equal to \frac{4}{5}. Find the ratio of the area of triangle ANL to the area of triangle ABC.

The volume of a frustum of a right circular cone is 52π cm*. Its altitude is
3cm and the measure of its lower radius is three times the measure of its
upper radius. the radius of upper base is 1.1547 cm and the slant height of the frustum is 3.7859 cm.
1. Find the lateral area of the frustum.

Find the volume of a right circular cone obtained from a sector of a circle in which the radius is 26 cm and the central angle is 138.5 ° ? Round your final answer to 1 decimal place.

an architect is designing a garden for a client on the planning sheet. The client requests the relocation of a water fountain by the rule (x,y) to (x+7,y-8). later, the client decides that they would prefer the water fountains location moved from this new position to units left and three units up. Find the composition as a single transformation

A monument is a stone structure in the form of a frustum of a regular square pyramid whose height is 50m and whose base
edges are 4.5m and 10m respectively. Through the center of the monument is a circular opening 3m in diameter at the top and
6m in diameter at the bottom.
1. What is the slant height of the opening?
2. What is the lateral surface area of the opening?
3. Find the volume of stone in the monument.

The volume of a frustum of a right circular cone is 52π cm*. Its altitude is
3cm and the measure of its lower radius is three times the measure of its
upper radius.
1. What is the radius of the upper base?
2. What is the slant height of the frustum?

A right circular cone is inscribed in a cube having a diagonal which
measures 20√3 cm.
1. What is the altitude of the cone?
2. What is the volume of the cone?
3. What is the surface area of the cone?

In the following fiNine students are seated evenly around a circular table. They are
marked on the circumference of the circle as A, B, C, D, E, F, G, H, I.
If the center of the circle is situated at point O, what is m<OAD