tg

tg
tgt

Saturday, 9 August 2014

chapter 4 Areas and Perimeters

Theorem 14
The area of a parallelogram is equal to bh where b is the length of its base and h is its height (the perpendicular distance from the base to the parallel side opposite).
Theorem 15
The area of a triangle is equal to \dfrac{1}{2}bh where b is the length of its base and h is its height (the perpendicular distance from the base to the vertex opposite).
Theorem 16 Heron’s Theorem
If the lengths of the sides of a triangle are ab and c, so that the semiperimeter s = (a + b + c)/2 then the area of the triangle is
\sqrt {s(s - a)\;(s - b)\;(s - c)}
Circles
Theorem 17
The area of a circle of radius r is \pi {r^2} and its circumference is 2\pi r.
Theorem 18
If AB is an arc of a circle then angles subtended at the circumference opposite AB are equal and are equal to half the angle subtended at the centre, i.e. in the diagram \angle ACB = \angle ADB = \dfrac{1}{2}\angle \,AOB.
Theorem 19
If AB is diameter of a circle and C is any point on the circumference of the circle then \angle ACB is a right angle.
Theorem 20
If A and B are points on the circumference of a circle with centre O and C is an exterior point of the circle such that BC is a tangent to the circle then \angle ABC = \dfrac{1}{2}\angle AOB.
Theorem 21
A line from the centre of a circle perpendicular to a chord bisects the chord and its arc.
Theorem 22
If A is a point on the circumference of a circle then a tangent to the circle at A is perpendicular to a radius of the circle to A.
Theorem 23
The two tangents drawn to a circle drawn from an exterior point of the circle have the same length.
Theorem 24
If two circles touch at a single point then this point and the centres of the circles are collinear.
Theorem 25
If two circles intersect at two points then the line through their centres is the perpendicular bisector of their common chord.
Theorem 26
Opposite angles of a cyclic quadrilateral sum to {180^ \circ } and if a pair of opposite angles of a quadrilateral sum to {180^ \circ } then it is cyclic.
Theorem 27
If XE is a tangent to the circle (X being any point on the plane of the circle) and ABCD are points on the circumference, we have the relations XA \cdot XB = XC \cdot XD = X{E^2}.

Post a Comment