In a trapezium PQRS, PQ is parallel to SR and ∠SPQ = ∠RQP = 135°. The trapezium contains an inscribed circle and the length of PQ is 1 cm. What is the exact length of QR? Need Urgently. Thanks
2026-04-12 21:36:55.1776029815
Problem Solving with a Trapezium - NEED HELP
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Refer to the following figure:
The radius of circle can be calculated from the small right triangle as :
$$\tan\left(\frac{135^\circ}{2}\right) = \frac{2r}{PQ} = 2r$$
Then QR is simply $2\sqrt{2}r$