Final answer:
The length of the chord BC in a circle with radius 25 cm and chords AB = AC = 60 cm is not present in the given options. Using the Pythagorean Theorem, the chord's length is calculated to be approximately 109.09 cm, which doesn't match any of the provided choices.
Step-by-step explanation:
Given that AB and AC are two chords in a circle with a radius of 25 cm and AB = AC = 60 cm, we want to find the length of the chord BC. Since AB = AC, we understand that triangle ABC is an isosceles triangle with AB = AC. Thus, by symmetry, the altitude from the center to the chord BC will bisect it, implying that triangles AOD and BOC (where O is the center and D is the midpoint of BC) are congruent right triangles. Using Pythagoras' theorem, the length of BD (which is half of BC) can be calculated as follows:
AD^2 = AB^2 - BD^2
25^2 = 60^2 - BD^2
625 = 3600 - BD^2
BD^2 = 3600 - 625
BD^2 = 2975
BD = \(\sqrt{2975}\) cm
BD \(\approx\) 54.55 cm
The length of chord BC is twice that of BD:
BC = 2 * BD \(\approx\) 2 * 54.55 cm
BC \(\approx\) 109.09 cm
Given the options, none exactly matches the calculated length of the chord. However, if there is a typo in the question and the radius was meant to be larger to be consistent with the chord length, a more accurate approximation or alternative method may be needed to reconcile this discrepancy.