the radii of two circles are 8cm and 12cm , while the distance between their centres is 15 cm. in how many point/s do these circles intersect ?
Answers
Answer:
it will intersect in 2 points...
Step-by-step explanation:
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Given:
The radii of the two circles are 8cm and 12cm respectively
The distance between their centers is 15cm.
To Find:
At how many points do these circles intersect.
Solution:
Let O be the center of the circle having a radius of 8cm and let O' be the center of another circle having a radius of 12cm. So, the distance OO' =15cm.
These two circles meet at points A and B. AB are the common chord of the circle.
Now, In ΔOAO'
OA² + O'A² = 8² + 12²
= 64 + 144
= 208
Then, OO'² = 15²
= 225
OA² + O'A² = OO'²
Hence, ∠OAO' = 90°
Area of a right-angled triangle OAO' = 1/2 × BASE × HEIGHT
= 1/2 × OA × O'A
Now, we substitute the values
= 8 × 12/2
= 48cm²
Area of the rhombus OAO'B = 2 × Area of a right-angled triangle OAO'
1/2 (AB × OO') = 2×48
1/2 × AB × 15 = 2 × 48
= 2 × 48 × 2/15
= 192/15
= 12.8cm
AB = 12.8cm
Therefore the measure of chord Ab is 12.8cm and it will intersect at two points.