Two circles of radii 10 cm and 8 cm intersect at the points P and Q. If PQ = 12 cm, and the distance between the centers of the
circles is x cm. The value of x (correct to one decimal place) is:
This questions was previously asked in
SSC CGL 4 June 2019 Shift-2
Explanation:
To solve this problem, you need to use geometry and algebra:
- Consider two circles intersecting at points P and Q.
- The radii of the circles are given as 10 cm and 8 cm.
- The distance PQ, which is a common chord of the circles, measures 12 cm.
- To find x, the distance between the centers, you can use the formula involving the power of the point:
\[
x = \sqrt{d_1^2 - (PQ/2)^2} + \sqrt{d_2^2 - (PQ/2)^2}
\]
\[
x = \sqrt{10^2 - 6^2} + \sqrt{8^2 - 6^2}
\]
\[
x = \sqrt{100 - 36} + \sqrt{64 - 36}
\]
\[
x = \sqrt{64} + \sqrt{28}
\]
\[
x = 8 + \sqrt{28}
\]
- Simplify \(\sqrt{28}\) to approximately 5.3, resulting in:
\[
x = 8 + 5.3 = 13.3
\]
- Option 2: 13.3 is the correct answer.
![]()
By: santosh