Q6 of 59 Page 73

In figure 3.59, altitudes YZ and XT of

∆ WXY intersect at P. Prove that,



(1) WZPT is cyclic.


(2) Points X, Z, T, Y are concyclic.


(1)In WZPT,


∠ WZP = ∠ WTP = 90° {YZ and XT are the altitudes}


If a pair of opposite angles of a quadrilateral is supplementary, then the


quadrilateral is cyclic.


⇒ WZPT is cyclic.


(2)∵ X, Z,T,Y lie on same circle, ∴ they are concyclic.


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