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

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Filo · Accepted Answer

PA & PB are the tangent to the circle with centre 'O'CD is a tangent to circle at E which intersects PA and PB in C & D respectively and PA=12cmLengths drawn from as External point to a circle are equal.So that PA=PB=12cmNow perimeter of ΔPCD=PC+CD+PD                                             =PC+(CE+ED)+PD    {∵CD=CE+ED}                                             =PC+(CA+DB)+PD    {∵  CA=CEDB=DE ​}                                             =(PC+CA)+(DB+PD)                                             =PA+PB    { PC+CA=PADB+PD=PB​}                                             =12cm+12cm                                             =24cmThus the perimeter of ΔPCD=24cm

Question Text	From an external point $P$ , tangents $P A$ and $PB$ are drawn to a circle with center $O$ . If $C D$ is the tangent to the circle at a point $E$ and $P A = 14$ cm, find the perimeter of the $△ PC D .$
Answer Type	Text solution:1
Upvotes	150

From an external point $P$ , tangents $P A$ and $PB$ are drawn to a circle with center $O$ . If $C D$ is the tangent to the circle at a point $E$ and $P A = 14$ cm, find the perimeter of the $△ PC D .$

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