## 03 Area inside the cardioid r = a(1 + cos θ) but outside the circle r = a

Example 3
Find the area inside the cardioid r = a(1 + cos θ) but outside the circle r = a.

## 01 Rectangle of maximum perimeter inscribed in a circle

Problem 01
Find the shape of the rectangle of maximum perimeter inscribed in a circle.

## C01 - Circle that is tangent to a given line with center at another given line

Problem 1
A circle is tangent to the line 2x - y + 1 = 0 at the point (2, 5) and the center is on the line x + y = 9. Find the equation of the circle.

## 08 Circles with diameters equal to corresponding sides of the triangle

Problem
From the figure shown below, O1, O2, and O3 are centers of circles located at the midpoints of the sides of the triangle ABC. The sides of ABC are diameters of the respective circles. Prove that

$A_1 + A_2 + A_3 = A_4$

where A1, A2, A3, and A4 are areas in shaded regions. ## 01 Arcs of quarter circles

Example 01
The figure shown below are circular arcs with center at each corner of the square and radius equal to the side of the square. It is desired to find the area enclosed by these arcs. Determine the area of the shaded region. ## 09 Dimensions of smaller equilateral triangle inside the circle

Problem
From the figure shown, ABC and DEF are equilateral triangles. Point E is the midpoint of AC and points D and F are on the circle circumscribing ABC. If AB is 12 cm, find DE. Conic Sections Jhun Vert Mon, 04/27/2020 - 04:35 pm

Definition
Conic sections can be defined as the locus of point that moves so that the ratio of its distance from a fixed point called the focus to its distance from a fixed line called the directrix is constant. The constant ratio is called the eccentricity of the conic. ## The Circle

The following are short descriptions of the circle shown below.

Tangent
Tangent is a line that would pass through one point on the circle.
Secant
Secant is a line that would pass through two points on the circle.
Chord
Chord is a secant that would terminate on the circle itself.
Diameter, d
Diameter is a chord that passes through the center of the circle. 