(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 = ?
Answers
Correct 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
(i) PA = 14 cm, find the perimeter of PCD.
(ii) If PA = 11cm, PD = 7 cm, then DE = ?
Answer:
(i) 28 cm
(ii) 4 cm
Explanation:
We know that
Two tangents drawn from an external point of a circle are equal in length
PA and PB are two tangents drawn to the circle from an external point P
⇒ PA = PB -- EQ( 1 )
AC and CE are two tangents drawn to the circle from an external point C
⇒ AC = CE -- EQ( 2 )
DE and DB are two tangents drawn to the circle from an external point D
⇒ DE = DB -- EQ( 3 )
(i) PA = 14 cm, find the perimeter of PCD.
From EQ( 1 ) and Given
⇒ PA = PB = 14 cm
Perimeter of PCD = Sum of all sides
= PC + PD + CD
From figure
= PC + PD + ( CE + DE )
From EQ( 2 ) EQ( 3 )
= PC + PD + ( AC + DB )
= ( PC + AC ) + ( PD + DB )
From figure
= PA + PB
= 14 + 14
= 28 cm
Hence, the perimeter ΔPCD is 28 cm.
(ii) If PA = 11cm, PD = 7 cm, then DE = ?
From EQ( 1 ) and given
⇒ PA = PB = 11 cm
Given, PD = 7 cm
From figure
⇒ DB = PB - PD = 11 - 7 = 4 cm
From EQ( 3 )
⇒ DB = DE = 4 cm
Hence the length of DE is 4 cm.
ʀᴇғᴇʀ ᴛʜᴇ ᴀᴛᴛᴀᴄʜᴍᴇɴᴛ.
ᴍᴀʀᴋ ʙʀᴀɪɴʟɪᴇsᴛ
ғᴏʟʟᴏᴡ ᴍᴇ
