Question

AB is a diameter of a circle and C is a point such that AC and BC are two chords of the circle. if AC =7cm and the radius of the circle is 12.5cm , then find BC .

Answer 1

If AB is a diameter of a circle and C is a point such that AC and BC are two chords of the circle,then <C will be 90.
B=7cm, H=AB=25cm
AC=P=sqroot(625-49)
=sqrt 576=24 cm

Answer 2

Answer:

BC is approximately 16.77 cm.

Step-by-step explanation:

Since AB is a diameter of the circle, the radius of the circle is half the length of AB. Therefore, the length of AB is:

AB = 2 × radius = 2 × 12.5 cm = 25 cm

We want to find the length of BC. To do this, we need to use the fact that the product of the lengths of the two segments of a chord is equal for any chord of a given circle. This is known as the power of a point theorem.

Using this theorem, we can write:

AC × CB = (AB/2)² - r²

where r is the radius of the circle.

Plugging in the values we know, we get:

7 cm × CB = (25 cm/2)² - (12.5 cm)²

Simplifying this equation, we get:

7 cm × CB = 156.25 cm² - 156.25 cm²/4

7 cm × CB = 117.1875 cm²

Dividing both sides by 7 cm, we get:

CB = 16.77 cm (rounded to two decimal places)

Therefore, BC is approximately 16.77 cm.

To learn more about diameter: https://brainly.in/question/54130688

To learn more about chords: https://brainly.in/question/631276

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