Similarity

Poblem #1:

[math]\text{Given a right-angled triangle ABC with a hypotenuse AB=25 cm and a leg BC=20 cm, \\ CD=15 cm (D lies on BC), DH is perpendicular to AB. \\ Find AH and HB.}[/math]

Pr. #1

Problem 2:

Given an isosceles triangle ABC with a leg 12 cm, an altitude to the base 8 cm. Find the radius of circumscribed circle (R)

Pr.#2:

Problem #3:

[math]\text{Find R-circumradius of triangle ABC, if AC=30 cm, BC=26 cm, an altitude CH=24 cm}[/math]

Pr. #3:

Problem 4:

Given an inscribed quadrilateral ABCD, AB=19 cm, BC=7 cm, CD=15 cm, AD=21 cm. The extensions of AB and CD intersect each other in point M. Find MB and MC.

Pr. #4:

Problem #5:

Given [math]\Delta[/math]ABC with a base 13 cm, the distance between the centroid G and the altitude CH to the base is 2 cm. Find AH and HB.

Pr.#5:

Problem #6:

Given [math]\Delta[/math]ABC with an altitude CH, AH=4 cm, HB=16 cm. Find the distance between the centroid G and the altitude CH