In the given figure, PR, RT and PT are tangents to the circle at Q, S and U respectively - Maths - Circles

Question

In the given figure, PR, RT and PT are tangents to the circle at Q,
S and U respectively
If PR = (RT + 3) cm, PR = (PT + 1) cm and perimeter of
âˆ†PRT is 26 cm, then QR + RT equal to:
(A) 9 cm (B) 7 cm (C) 13 cm (D) 11 cm

Brijendra Pal · Accepted Answer

Hi, perimeter of triangle PRT = 26 cm PR+RT+PT = 26 PR+PR-3+PR-1 = 263PR= 30 PR = 10 cm so RT = 7 cm and PT = 9 cm now we know that tangents from external point to circle are equalso lets say RS = SQ = x PQ= PU =  y TU= TS = z x+y = RP = 10 
1y+z= PT = 9 
2z+x= RT = 7 
3add all 2x+y+z= 26 x+y+z = 13 
4subtracting equation 1,2,3 one by one from equation 4 z =3, x = 4,y = 6 so QR+RT = x+7 = 4+7 = 11 cm

In the given figure, PR, RT and PT are tangents to the circle at Q, S and U respectively. If PR = (RT + 3) cm, PR = (PT + 1) cm and perimeter of ∆PRT is 26 cm, then QR + RT equal to: (A) 9 cm (B) 7 cm (C) 13 cm (D) 11 cm

In the given figure, PR, RT and PT are tangents to the circle at Q, S and U respectively.
If PR = (RT + 3) cm, PR = (PT + 1) cm and perimeter of ∆PRT is 26 cm, then QR + RT equal to:
(A) 9 cm (B) 7 cm (C) 13 cm (D) 11 cm