Question

D is centre of a circle with radius 5cm. T is a point such that OT = 13 cm and OT intersects circle at E. If AB is tangent to a circle at E. then find length AB.

Answer 1

Step-by-step explanation:

Clearly ∠OPT=90o

Applying Pythagoras in △OPT, we have

OT2=OP2+PT2

⇒132=52+PT2

⇒PT2=169−25=144

⇒PT=12 cm

Since lengths of tangents drawn from a point to a circle are equal. Therefore,

AP=AE=x(say)

⇒AT=PT−AP=(12−x)cm

Since AB is the tangent to the circleE. Therefore, OE⊥AB

⇒∠OEA=90o

⇒∠AET=90o

⇒AT2=AE2+ET2 [Applying Pythagoras Theorem in △AET]

⇒(12−x)2=x2+(13−5)2

⇒144−24x+x2=x2+64

⇒24x=80

⇒x=