Question 93
In the given figure. QRTS is a cyclic quadrilateral. If PT = 5 cm. SQ= 4 cm. PS = 6 cm and ∠PQR = 63°. then what is the value (in cm) of TR?
Solution
In cyclic quadrilateral QRTS,
∠PQR + ∠STR = 180°
$$\Rightarrow$$ 63° + ∠STR = 180°
$$\Rightarrow$$ ∠STR = 127°
$$\Rightarrow$$ ∠STR + ∠STP = 180°
$$\Rightarrow$$ ∠STP = 180° - 127° = 63°
Triangle PST ~ triangle PQR,
PQ/PT = PR/PS
$$\Rightarrow$$ (PS + SQ)/PT = PR/PS
$$\Rightarrow$$ 10/5 = PR/6
PR = 12
TR = PR - PT = 12 - 5 = 7
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