Angles - points, lines and parallel lines

Weekly Problem 23 - 2008
A triangle has been drawn inside this circle. Can you find the length of the chord it forms?

This diagram has symmetry of order four. Can you use different geometric properties to find a particular length?

On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?

ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.

Six circles around a central circle make a flower. Watch the flower as you change the radii in this circle packing. Prove that with the given ratios of the radii the petals touch and fit perfectly.

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?

Which hexagons tessellate?

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

How many right angles can you make using two sticks?