Two trees 20 metres and 30 metres long, lean across a passageway between two vertical walls. They cross at a point 8 metres above the ground. What is the distance between the foot of the trees?
Three triangles ABC, CBD and ABD (where D is a point on AC) are all
isosceles. Find all the angles. Prove that the ratio of AB to BC is
equal to the golden ratio.
ABCD is a rectangle and P, Q, R and S are moveable points on the
edges dividing the edges in certain ratios. Strangely PQRS is
always a cyclic quadrilateral and you can find the angles.
$ICH$ is an isosceles triangle which can be split into two
congruent right angled triangles by drawing line $CJ$, where $J$ is
the midpoint of chord $IH$.
Triangle $AJC$ is similar to triangle $AGD$, with a ratio of 6
cm to 10 cm or 3:5.
Line $GD = R= $2 cm,
Line $CJ =$ 3/5 $GD= $1.2 cm.
This is Gordon's proof of the general case of n circles
where $AG$ cuts the m th circle at $I$ and