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  2. Tangent lines to circles - Wikipedia

    en.wikipedia.org/wiki/Tangent_lines_to_circles

    Let O 1 and O 2 be the centers of the two circles, C 1 and C 2 and let r 1 and r 2 be their radii, with r 1 > r 2; in other words, circle C 1 is defined as the larger of the two circles. Two different methods may be used to construct the external and internal tangent lines. External tangents Construction of the outer tangent

  3. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    This allows the two congruent purple-outline triangles and to be constructed, each with hypotenuse ⁡ and angle at their base. The sum of the heights of the red and blue triangles is sin ⁡ θ + sin ⁡ φ {\displaystyle \sin \theta +\sin \varphi } , and this is equal to twice the height of one purple triangle, i.e. 2 sin ⁡ p cos ⁡ q ...

  4. Law of sines - Wikipedia

    en.wikipedia.org/wiki/Law_of_sines

    In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law, ⁡ = ⁡ = ⁡ =, where a, b, and c are the lengths of the sides of a triangle, and α, β, and γ are the opposite angles (see figure 2), while R is the radius of the triangle's circumcircle.

  5. Exact trigonometric values - Wikipedia

    en.wikipedia.org/wiki/Exact_trigonometric_values

    Since two of the angles in an isosceles triangle are equal, if the remaining angle is 90° for a right triangle, then the two equal angles are each 45°. Then by the Pythagorean theorem, the length of the hypotenuse of such a triangle is 2 {\displaystyle {\sqrt {2}}} .

  6. Circular arc - Wikipedia

    en.wikipedia.org/wiki/Circular_arc

    A circular sector is shaded in green. Its curved boundary of length L is a circular arc. A circular arc is the arc of a circle between a pair of distinct points.If the two points are not directly opposite each other, one of these arcs, the minor arc, subtends an angle at the center of the circle that is less than π radians (180 degrees); and the other arc, the major arc, subtends an angle ...

  7. Millions hurt by credit repair firms to share $1.8 billion in ...

    www.aol.com/millions-hurt-credit-repair-1...

    More than 4 million Americans gouged by credit repair companies including Lexington Law and CreditRepair.com will soon collectively receive $1.8 billion in refund checks, the Consumer Financial ...

  8. Some U.S. grocery prices are dipping for the first time since ...

    www.aol.com/u-grocery-prices-dipping-first...

    Grocery prices continue to eat a hole in household budgets, with many Americans citing the economy and inflation as top issues behind their votes in the November 5 election. But there are signs ...

  9. Sources: Rice fires head coach Mike Bloomgren following loss ...

    www.aol.com/sports/sources-rice-fires-coach-mike...

    The season before, Rice got to a bowl game despite a 5-7 season because there weren’t enough 6-6 teams and the Owls had one of the best Academic Progress Rates of any 5-7 team.