Question

In circle O, BC =19 and DC=35. The diagram is not to scale.

what is the length of diameter BA?.

Answer 1

1. CD is tangent to the circle with center O, at point D.

2. Join D to O.

3. OD = OB = r, where r is the radius of the circle.

4. radius OD is perpendicular to the tangent CD.

5. Thus in the right triangle OCD:
`CD^(2) + DO^(2) = CO^(2)`, by the pythagorean theorem.

6.
`(19+r)^(2)= 35^(2)+ r^(2)`


`38r=35 ^(2)-19^(2)`

Note: when applying pythagorean theorem, the difference of squares property
[
`a ^(2) -b^(2) =(a-b)(a+b)` ] is a useful practical tool in calculations.

38r=(35 -19)(35+19)
38r=16*54

r=
`(16*54)/(38)= 22.74`

7. Finally, the diameter BA=2r=2*22.74=45.48

So the answer is 45.5