Three by One
ABCD is a rectangle where BC = 3AB. P and Q are points on BC such that BP = PQ = QC.
Show that: angle DBC + angle DPC = angle DQC
Generalise this result.
N.B. This problem can be tackled in at least 8 different ways using different mathematics learnt in the last two years in school and earlier. The methods are essentially the same when viewed from a more advanced perspective.
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