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For each of the following, a wellknown phrase has been divided into groups of three letters that have then been placed in the wrong order. Find all the six phrases.
(i) EST, HON, OBI,LTW, ONE, RDS, WIT, KIL
(ii) EBU, EHO, ETH, LLB, RNS, TAK, YTH
(iii) ATO, EAC, INR, LIK, NAH, OOF, OTT
(iv) USH, NTH, ABI, HEB, SWO, RDI, INT, NDI, RTH, TWO, EHA
(v) OKA, ACA, ING, TAK, YLO, TMA
(vi) OBL, HAL, HAR, APR, LEM, VED, SAP, EDI, EMS, ROB
Take any convex quadrilateral ABCD, with diagonals AC and BD. Pick E so ABCE is a parallelogram. Prove that AB²+BC²+CD²+DA²= AC²+BD²+DE². Given the same quadrilateral, let P and Q be the midpoints of AC and BD. Now prove that AB²+BC²+CD²+DA²= AC²+BD²+4PQ².
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