1) imagine a circle with a chord, now imagine a line that is drawn from the centre perpendicular to the chord. this is the situation here however i am making the assumption that the chord is perpendicular to the line from the centre and the line from the centre meets at the centre of the chord.
A right angled triangle with base 12 inches and height 9 inches. use Pythagoras to find the radius,
radius = sqroot(12^2 + 9^2) = sqroot(144 + 81) = sqroot(225) = 15 inches
2) in this question draw a regular hexagon and then a circle around it. the diameter is the length from of one of the vertices to the opposite one.
the hexagon can be split into 6 triangles by drawing lines between the centre and the vertices, these triangle are equilateral as the angles in them are 60 degrees [360/6 = 60]
therefore the radius is equal to the length of the sides of the triangles which it 12/2 = 6cm
3) here the triangle can be split into 3 isosceles triangles. the two bottom angles being 30 degrees. meaning the other angle be 120 degrees. the base has length 18cm
using the cosine rule to find the length of other two sides which are equal to the radius of the cirlce.
find the arc length by multiplying the circumference of the circle by 120/360 which is the proportion of the circle you want.
drawing a diagram for each question helps to see what i am explaining!
