construct a quadrilateral PQRS in which angle p -120 degree, angle Q -80 degree, angle R - 70 degree and PQ- QR-5. 2 cm
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Step-by-step explanation:
By Pythagoras' theorem,
PR
2
=PQ
2
+QR
2
PR
2
=24
2
+7
2
=576+49=625
∴PR=25 cm
Let the inradius of △PQR be x cm.
□OAQC is a square. Hence QA=x cm and AR=(7−x) cm
RA and RB act as tangents to the incircle from point R, hence their lengths are equal. ∴RB=AR=(7−x) cm.
Similarly, PB=PC=(24−x) cm
PR=PB+RB
⇒25=(24−x)+(7−x)
⇒25=31−2x
⇒x=3 cm
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