Two circles of radii 13cm and 5cm intersect at two points in such a way that the distance between their centres is 12cm. Find the length of the common chord of the two circles.
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Answers
Given:
Two circles of radii 13 cm and 5 cm intersect at two points in such a way that the distance between their centers is 12 cm.
To find:
Find the length of the common chord of the two circles.
Solution:
From the given information, we have the data as follows.
Two circles of radii 13 cm and 5 cm intersect at two points in such a way that the distance between their centers is 12 cm.
Consider the attached figure while going through the following steps.
From the figure, ABC represents a triangle.
The area of Δ ABC is given as follows.
Δ ABC = √ [ s (s - a) (s - b) (s - c) ]
Here, s = (AB + BC + CA)/2
s = (13 + 5 + 12)/2
s = 15 cm.
Substitute the values in the above equation.
Δ ABC = √ [ s (s - a) (s - b) (s - c) ]
Δ ABC = √ [ 15 (15 - 13) (15 - 5) (15 - 12) ]
Δ ABC = 30 cm
The area of Δ ABC is given by the formula as follows.
Δ ABC = 1/2 × AB × L
30 = 1/2 × 12 × L
30 = 6 L
L = 5 cm.
Therefore, the length of the common chord of the two circles is 5 cm.
