Geometry, Plane figures solved problems

Geometry - Plane Figures Problems and Solutions

Plane figures, solved problems, examples

Example: Deltoid with sides length of 1 and 2 is inscribed into a circle. The ratio of greater to the shorter diagonal is?

Solution: Given a = 2 and b = 1. e : f = ?

Example: One side of a parallelogram is 4 cm, other 6 cm, and the diagonal 4Ö2 cm, length of the other diagonal is?

Solution: Given a = 6 cm, b = 4 cm and d₁ = 4Ö2 cm . d₂ = ?

Example: Find the area of the rhomb (diamond) with the side of length 20 cm and the diagonal of length 32 cm.

Solution: Given a = 20 cm and e = 32 cm. A _rhombus = ?

Example: Length of the side of the right decagon is 12. Find the radius of its circumcircle.

Solution: Given n = 10 and a = 12. r = ?

Example: In a circle with the radius 2 cm, on its chord 2Ö2 cm long taken as a diameter, constructed is another circle. The area of the part of that circle, which is outside of the greater circle, is?

Solution: Given r = 2 cm and t = 2Ö2 cm. A = ?

Example: Distance of centers of circles with radii, 20 cm and 10 cm, is 50 cm. Their common external tangent touches one circle at a point D₁ and other at D₂. Find the length of the segment D₁D₂.

Solution: Given r₁ = 20 cm, r₂ = 10 cm and S₁S₂ = 50 cm . D₁D₂ = ?

Example: The chord of a circle is long 12 cm and cuts of the circle segment whose height is 3 cm. Find the radius of the circle. Height of the segment equals the difference between the radius of the circle and the distance of the chord from the circle’s center.

Solution: Given t = 12 and h = 3. r = ?

Example: The perimeter of a circle is divided to the four parts whose arcs relate as 1: 2 : 4 : 5, what are the values of the corresponding central angles?

Solution: Given arcs relationship, 1: 2 : 4 : 5. the corresponding central angles ?

Geometry and use of trigonometry contents - A