Looking at the modified drawing, recall the secant theorem.
(AC)(BC)=(EC)(DC). Then solve for x.
thank you plato!
and soroban!
however i find using plato's secant theorem being the easier:
since:
(AC)(BC)=(EC)(DC).
(18)(10)=(10+x)(x)
=x^2+10x
x^2+10x-180=0
(-10 +/- sq.root 82) / 2
and since we need a positive value we do:
(-10 + sq.root 82) / 2
= 9.317821063....
and add the 5cm radius to get OC
= 14.3cm(1dp)
=sq. root 205 as soroban said
Thanks for the help!
That is also my method except that I didn’t use trigonometry. By Pythagoras’ theorem on triangle ODA, OD = = 3 cm. By Pythagoras’ theorem on triangle ODC, OC = cm.
You made a mistake there; it should be 820, not 82. It’s also easier to make mistakes with your calculations using the secant method. My recommendation: use the method that Soroban and I used.