In the given figure QRTS is a cycle quadrilateral if PT 5cm SQ 4cm PS 6cm and angle P...........

Quantitative Aptitude (CGL) Coordinate Geometry

In the given figure QRTS is a cycle quadrilateral if PT=5cm, SQ=4cm , PS=6cm and angle PQR=63 then what is the value of TR?

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Explanation:

QRTS is a cyclic quadrilateral. In triangle PTS, PT = 5 cm, PS = 6 cm, PS/sin 63 = PT/sin PST = TS/sin P, or
6/sin 63 = 5/sin PST, or
sin PST = 5 sin 63/6 = 0.742505436 or PS/sin 63 = TS/sin P, or TS = PS*sin P/sin 63 = 6* sin 69.05472005/sin 63 = 6.288992726 cm
In triangle PQR, PQ/sin QRT = RP/sin PQR, or
10/sin 47.94527995 = RP/sin 63, or
RP = 10*sin 63/sin 47.94527995 = 12.
Therefore TR = RP - TP = 12 - 5 = 7 cm