Q. 143.7( 3 Votes )

(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 = ?


Answer :

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


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