Chord AB of a circle of radius 10 cm is at a distance 8 cm from the centre O. If tangents drawn at A and B intersect at P, then the length of the tangent AP (in cm) is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 7.5
By using Pythagoras theorem in triangle OAD one gets,
AD2 = 100 - 64 = 36.
AD = 6cm so AB = 12 cm.
Let PD = x cm.
In triangle OAP,
⇒ OA2 + AP2 = OP2
⇒ 100 + AP2 = (x + 8)2.
⇒ AP2 = x2 + 16x - 36.......(1)
Now in Triangle DAP,
⇒ AD2 + PD2 = AP2
⇒ 36 + x2 = AP2 ..............(2)
By using eq 1 and 2 we get
⇒ 36 + x2 = x2 + 16x - 36
⇒ x = 4.5 cm
⇒ 36 + 20.25 = AP2
⇒ AP = 7.5 cm.