## 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*.

**Example 3**

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

**Problem 01**

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

**Problem 1**

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

**Problem**

From the figure shown below, O_{1}, O_{2}, and O_{3} 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 A_{1}, A_{2}, A_{3}, and A_{4} are areas in shaded regions.

**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.

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**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

**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.

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The following are short descriptions of the circle shown below.

- Read more about The Circle
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