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標題:

concyclic question

發問:

The figure shows the circumcircle of △ABC. TQAC is a straight line. PQ, PR and PS are three altitudes. ∠QPR = 66°, ∠PQR=32° and ∠ACB = 58°. It is give that A,Q,P and R are concyclic. a)Show that B,P,R and S are concyclic. b)Hence find ∠ABC and ∠ABP. http://img220.imageshack.us/i/0003jx.jpg/

最佳解答:

(a) ∠QAR = 180 - 66 = 114∠ABC = 180 - 66 - 58 = 56∠ASC = 90 - (180 - 58 - 58) = 26∠SPR = 180 - 26 - 32 - 66 = 56So, ∠ABC = ∠SPRB,P,R and S are concyclic (Converse of ∠ in the same segment)(b) ∠ABC = 180 - 66 - 58 = 56 by the resulyt of (a)∠PRS = 180 - 26 - 56 = 96∠PBS = 180 - ∠PRS = 84∠ABP = ∠PBS - ∠ABC = 84 - 56 = 28 2011-03-01 21:49:47 補充： GOOD。我解題時沒有留意。

其他解答:

Faster method to solve (a) (a) ∠BRP = ∠BSP = 90 deg B,P,R and S are concyclic. (converse of ∠ in the same segment)B5117735D6B60D95