two circles of radii 10 cm and 17 cm intersect at two points and distance between their centers is 21 cm.find length of common chord
Make a sketch.
draw a radius from the each of the circles to the points of contact of the common tangent.
Those two radii will be parallel
joint the two centres.
draw a perpendicular from the centre of the smaller circle to the larger radius.
You will see a right-angled triangle with hypotenuse 21, one short side of 7 and the other leg will be the length of the common tangent.
x^2 + 7^2 = 21^2
x^2 = 392
x = √392 = .....
To find the length of the common chord between two intersecting circles, we can use the intersecting chord theorem. This theorem states that when two circles intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.
In this case, we have two circles with radii of 10 cm and 17 cm. The distance between their centers is 21 cm.
Let's label the centers of the circles as O1 and O2, with the radii r1 = 10 cm and r2 = 17 cm, respectively.
From the given information, we know that the distance between the centers of the circles (O1O2) is 21 cm.
Now, let's draw the line segment connecting the centers of the circles (O1O2), and label the points where this line intersects the circles as P1 and P2.
Since O1P1 and O2P2 are the radii of the circles, we can calculate their lengths as follows:
O1P1 = r1 = 10 cm
O2P2 = r2 = 17 cm
Now, we need to find the length of the common chord, which is represented by the line segment P1P2.
Using the intersecting chord theorem, we can calculate the length of the common chord as follows:
O1P1 * O1P2 = O2P1 * O2P2
10 cm * O1P2 = 17 cm * 21 cm
10 cm * O1P2 = 357 cm
O1P2 = 357 cm / 10 cm
O1P2 = 35.7 cm
Therefore, the length of the common chord (P1P2) is approximately 35.7 cm.