(i) 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 = 14 cm, find the perimeter of PCD.(ii) If PA = 11cm, PD = 7 cm, then DE = ?

i) From P we have tangents PA and PB

Hence PA = PB …tangents from same point are equal …(a)

Point C is on PA

From C we have tangents CA and CE

CA = CE …tangents from same point are equal …(i)

Point D is on PB

From D we have two tangents DE and DB

DE = DB … tangents from same point are equal …(ii)

Consider ΔPCD

perimeter of ΔPCD = PC + CD + PD

From figure CD = CE + ED

perimeter of ΔPCD = PC + CE + ED + PD

Using (i) and (ii)

perimeter of ΔPCD = PC + CA + DB + PD

From figure we have

PC + CA = PA and DB + PD = PB

perimeter of ΔPCD = PA + PB

Using (a)

perimeter of ΔPCD = PA + PA

perimeter of ΔPCD = 2(PA)

PA is 14 cm given

perimeter of ΔPCD = 2 × 14

perimeter of ΔPCD = 28 cm

ii) PA = 11 cm …given

using (a)

PB = 11 cm

From figure

PB = PD + DB

Using (ii)

PB = PD + DE

11 = 7 + DE …PD is 7 cm given

DE = 5 cm

Hence DE = 5 cm

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz | Testing Your Knowledge on Circles32 mins
Quiz | Imp. Qs. on Circle35 mins
Important Questions on Circles46 mins
Smart Revision | Circles44 mins
Quiz | Imp. Qs. on Circles37 mins
RD Sharma | Important Questions on Circles36 mins
Short Cut Trick to Find Area of Triangle43 mins
Tangent from an External Point54 mins
RD Sharma | Most Important Questions of Circles35 mins
RD Sharma | Imp Qs Discussion on Area Related With Circles41 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses