Geometry Answers

prove that two chords of a circle are congruent if and only if they subtend arcs of equal measure.

Angle bisectors of angles BAC and BCA of triangle ABC intersect its altitude BH at points P and

Q respectively. It is known that point H lies on side AC, P is situated between H and Q,

BQ = 54,5, QP = 17,5, PH = 36. Find the area S of triangle ABC. As the answer,

indicate the value of S√3 .

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 ANL, BKN and CLK to the area of triangle ABC are equal to

5/33 , 9/44 and 5/12 respectively. Find the ratio of IK : AI.

A concrete monument is a regular pentagonal pyramid with base edge of
40 cm and one of its lateral edges measure 50 cm. if the height is 36.64cm and lateral surface is 916.52 centimeter squared.
1. How much concrete is needed to build the monument?

An inverted regular square pyramid has an altitude of 12m and with top
edge of 3m is fully–filled with water.
1. What is the volume of the water in m3?
A portion of water is to be removed so that water will be 7m deep.
2. What is the area at the surface of the water when it is 7m deep?
3. How much water is to be removed so that water is 7m deep?
4. How much water retained when it is 7m deep?

Given: PS = RT, PQ = ST
Prove: QS = RS

Line l touches the circle w at point K. Points A and B are chosen on w in such a way that they are

situated on opposite sides with respect to the diameter of w that passes through point K. Find the area of triangle AKB if the distances from points A and B to line l are equal to 6 and

9 respectively, and AK = 10. 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 8/35 and
1/7 respectively, and ratio IK : AI is equal to 2/7. Find the ratio of the area of triangle
ANL to the area of triangle ABC.