If PQ is tangent to circle R at point Q and PS is
1 answer:
Answer:
Perimeter of the quadrilateral PQRS is 25 units
Step-by-step explanation:
From the figure attached,
PQ is a tangent to the given circle so m∠PQR = 90°
Now we apply Pythagoras theorem in the ΔPQR,
PR² = PQ² + QR²
(PT + TR)²= PQ² + 5²
(4 + 5)² = PQ² + 25
81 = PQ² + 25
PQ = √(81 - 25)
= √56
≈ 7.5 units
PQ ≅ PS ≅ 7.5 units
[Since measures of tangents drawn from a point to a circle are always equal]
Perimeter of PQRS = PQ + QR + RS + PS
= 7.5 + 5 + 5 + 7.5
= 25 units
Therefore, perimeter of the quadrilateral PQRS is 25 units.
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