In the given figure, PQ and PR are two tangents drawn from an external point P to a circle with centre 'O'. If OQ = 3 cm and PS = 2cm then, find the perimeter (in cm) of quadrilateral PQOR.
OQ = OR = 3 cm
PO = PS + OS = 2 + 3 = 5 cm
By Theorem- The tangent at any point of a circle is perpendicular to the radius through the point of contact.
We know that PQ and PR are tangents, hence
∠PQO = ∠PRO = 90∘
Now, applying pythagoras theorem in right △ OQP
PO2=PQ2+OQ2
PQ2=52−32
PQ = 4 cm
Thus PQ = PR = 4cm ( By Theorem- Tangents drawn from an external point to a circle are equal in length)
Perimeter of quadrilateral PQOR is sum of all sides
= PQ + PR + OQ + OR
= 4 + 4 + 3 + 3
= 14 cm