Given information:
- Chords AB and CD subtend equal angles of 70 degrees at the center O of the circle.
- OK is perpendicular to AB.
- AL = 2.5 cm.

To find: CD

Solution:
Let's draw a diagram for better understanding.



Angle subtended by chord at center:
- The angle subtended by chord AB at the center O is 70 degrees.
- Similarly, the angle subtended by chord CD at the center O is also 70 degrees.

Angle subtended by chord at circumference:
- The angle subtended by chord AB at the circumference is half of the angle subtended at the center.
- Therefore, the angle subtended by chord AB at point A or B on the circumference is 35 degrees.
- Similarly, the angle subtended by chord CD at point C or D on the circumference is also 35 degrees.

Right triangle:
- Triangle AOK is a right triangle since OK is perpendicular to AB.
- Therefore, we can use trigonometry to find out the length of OK.

Using trigonometry:
- Let's assume the length of OK is x cm.
- We know that tan(35) = AL / OK = 2.5 / x (since AL = 2.5 cm)
- Therefore, x = 2.5 / tan(35) = 3.94 cm (approx.)

Length of chord CD:
- Let's assume the length of CD is y cm.
- Since chord AB and chord CD subtend equal angles at the center, they are equal in length.
- Therefore, AB = CD = 2 * radius (where radius is the distance from the center O to any point on the circumference)
- We know that OK is perpendicular to AB, and it bisects AB (since angle subtended by AB at the center is 70 degrees).
- Therefore, AK = KB = AB / 2 = radius.
- In triangle CKO, we can use trigonometry to find out the length of CK (which is half of CD).
- We know that cos(35) = CK / OK = (2 * radius - y) / x
- Therefore, CK = x * cos(35) + y - 2 * radius
- Substituting the value of x, we get CK = 0.82 + y - 5 = y - 4.18
- Since CK = CD / 2, we get CD = 2 * CK = 2 * (y - 4.18) = 2y - 8.36

Final answer:
- CD = 2y - 8.36
- We don't know the value of y, so we cannot find the exact value of CD.
- However, we have expressed CD in terms of y, so we can find CD if we know the value of y.