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

Answer:

angle opt is 90 degree

13^2=5^2+PT^2

PT^2=‌‌169-25=24

PT=12

Since the lenghts are equal

therefore,

AP=AE=x(let it be)

Since, AB is tangent to circle E.

therefore,

angle OEA=90 degree= angle AET =90 degree

therefore,(12-x)^2=x^2+(13+5)^2

144-24x+x^2=x^2+64

24x=80

x=80/24

x=10/3

therefore,

AB=AE+BE

=(10/3+10/3)cm

=20/3cm

HOPE IT HELPS