Question

From an external point P, tangents PA and PB are drawn to a circle with centre O. If CD is the tangent to the circle at the point E and PA = 14cm, find the perimeter of ΔPCD.

Answer 1

Given that,

PA and PB are tangents to circle. 

And we know that lengths of tangents drawn from same external point are always equal. 

∴ PA = PB, 

(PA & PB are tangents to circle from point P) 

AC = CE, 

(AC & CE are tangents to circle from point C) 

BD = DE. 

(BD & DE are tangents to circle from point D) 

Now, 

PA = PC + AC = PC + CE 

(∵BD = DE) 

∴ PC = PA – CE … (1) 

And,

PB = PD + BD = PD + DE 

(∵ BD = DE) 

∴ PD = PB – DE … (2) 

Now,

Perimeter of ΔPCD = PC + CD + PD 

= (PA – CE) + (CE + DE) + (PB – DE) 

(From equations (1) & (2) and CD = CE + DE) 

∴ Perimeter of ΔPCD = PA + PB 

= 2PA 

= 2×14 

= 28cm. 

(∵ PA = PB = 14 cm) 

∴ The perimeter of triangle PCD is 28 cm.