From an outside point P, two tangents, PA and PB, are drawn to a circle. A third tangent to the circle at a point Q intersects PA and PB at R and S, respectively. If PA = 10 cm, what is the perimeter of PRS?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 20 cm.
PA = PB = 10 cm
From the tangent property:
RA = RQ
SB = SQ
Also,
⇒ PA = PR + RA = 10 cm
⇒ PB = PS + SB = 10 cm
⇒ RS = RQ + QS = RA + SB
Perimeter of △PRS = PR + PS + RS = PR + PS + RA + SB
⇒ (PR + RA) + (PS + SB) = 10 + 10 = 20 cm