Question

Plzz tell a short method

Answer 1

sry the answer is not in short...so try to understand...

AB=12 cm and BC = 12 cm radius OA =10 cm(join OA)
join OB and mark M at the intersection
so,BM perpendicular to AC
ABC is an isoceles triangle as AB = AC
(now, we have all the information)

let AM =y and OM = x then BM = 10-x
applying Pythagoras theorem in triangle AMB
AB^2=BM^2+AM^2
12^2=(10-x)^2+y^2 (1)

applying Pythagoras theorem in triangleOAM
OA^2=OM^2+AM^2
10^2=x^2+y^2. (2)
substract 1 from 2

100-144=(10-x)^2-x^2
-44=100-20x
-100-44=-20x
-144=-20x
144/20=x
7.2=x(approx)

substituting the value of X in 2
100=7.2^2+y^2
100-51.84=y^2
48.16=y^2
6.9=y(approx)
AC=2y
=2×6.9=13.8cm
distance b/w A and C = 13.8cm

hope it's clear to you...