30 Questions
What is the formula for cos A in a triangle ABC?
cos A = b^2 + c^2 - a^2 / 2bc
What is the formula for tan B in a triangle ABC where R is the radius of the circumcircle?
tan B = R(b + c - a) / 2
What is the formula for the square of side a in a triangle ABC?
a^2 = b^2 + c^2 - 2bc cos A
What is the formula for sin A in a triangle ABC where R is the radius of the circumcircle?
sin A = a / 2R
What is the formula for the square of side b in a triangle ABC?
b^2 = c^2 + a^2 - 2ca cos B
What is the formula for the area of a triangle, with sides a, b, and c?
$\sqrt{s(s-a)(s-b)(s-c)}$
What is the formula for sine of an angle in a triangle ABC?
$\frac{(s-b)(s-c)}{bc}$
What is the formula for cosine of an angle in a triangle ABC?
$\frac{(s-a)(s-c)}{bc}$
What is the formula for tangent of an angle in a triangle ABC?
$\frac{(s-c)}{(s-a)(s-b)}$
What is the sum of the squares of the altitudes of a triangle ABC, in terms of the area of the triangle?
$\frac{a^2+b^2+c^2}{\Delta}$
If two sides and the included angle of a triangle are given, what is the formula to find the area of the triangle?
$\frac{1}{2}bc\sin A$
If three sides of a triangle are given, what is the formula to find the area of the triangle?
$\sqrt{s(s-a)(s-b)(s-c)}$
If three sides and the circum-radius of a triangle are given, what is the formula to find the area of the triangle?
$\frac{abc}{4R}$
If $a = 2x$, $b = 2y$, and $C = 120^\circ$ in a triangle, what is the area of the triangle?
$3xy$
If $a = 2$, $b = c$, and $\cos A = \cos B = \cos C$ in a triangle, what is the area of the triangle?
$2$
What is the point where the perpendicular bisectors of the sides of a triangle intersect?
The circumcentre
What is the radius of the circle that can be inscribed within a triangle denoted by?
r
What is the formula for the circum-radius of a triangle?
R = (abc) / (4Δ)
What passes through the angular points of a triangle?
Circumcircle
What is the centre of the inscribed circle of a triangle?
The incentre
What is the ratio of the area of a circle to the area of a regular polygon of n sides, where the perimeter of the circle is equal to the perimeter of the polygon?
$\pi : \tan(\pi/n)$
If a is the length of each side of a regular polygon of n sides, what is the sum of the radii of the inscribed and circumscribed circles?
$a\cot(\pi/n) + a\tan(\pi/n)$
If a is the length of each side of a regular polygon of n sides, what is the radius of the inscribed circle?
$a\cot(\pi/n)$
What is the formula for the area of a regular polygon of n sides, where a is the length of each side?
$\frac{n\pi a^2}{4\tan(\pi/n)}$
If a is the length of each side of a regular polygon of n sides, what is the radius of the circumscribed circle?
$a\sin(\pi/n)$
What is the radius of the inscribed circle of a triangle ABC?
r = (s - a) tan A/2
What is the centre of the escribed circle opposite to the angle A in a triangle ABC?
The point of intersection of the external bisectors of angles B and C
If r1, r2, and r3 are the radii of the escribed circles opposite to the angles A, B, and C respectively, what is the relationship between them?
r1 = r2 = r3
What is the condition for the existence of an escribed circle opposite to the angle A in a triangle ABC?
AB + AC > BC
If R is the circumradius of a triangle ABC, what is the relationship between the inradius r and R?
r = R/2
Test your understanding of triangle properties, including formulas and equations. Solve problems involving triangles and their sides, angles, and trigonometric functions.
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