This problem can be solved using the properties of right triangles and the properties of circles.

Step 1: Draw a diagram. Draw two circles with centers X and Y and radii 9 cm and 2 cm respectively. Draw a line segment XY of length 17 cm. Draw a third circle with center Z and radius r cm that touches the other two circles externally. Draw a line segment from X to Z and from Z to Y, forming a right triangle XYZ.

Step 2: Apply the Pythagorean theorem. Since triangle XYZ is a right triangle, the square of the length of the hypotenuse (XY) is equal to the sum of the squares of the lengths of the other two sides (XZ and ZY).

Step 3: Use the properties of circles. The length of XZ is the sum of the radii of the circles with centers X and Z, or 9 cm + r cm. The length of ZY is the sum of the radii of the circles with centers Z and Y, or r cm + 2 cm.

Step 4: Substitute these lengths into the Pythagorean theorem. (9 cm + r cm)^2 + (r cm + 2 cm)^2 = (17 cm)^2.

Step 5: Solve for r. This is a quadratic equation in r, which can be solved by factoring, completing the square, or using the quadratic formula. The solution is r = 6 cm.

So, the correct choice is 6 cm.

Question

This problem can be solved using the properties of right triangles and the properties of circles.

Step 1: Draw a diagram. Draw two circles with centers X and Y and radii 9 cm and 2 cm respectively. Draw a line segment XY of length 17 cm. Draw a third circle with center Z and radius r cm that touches the other two circles externally. Draw a line segment from X to Z and from Z to Y, forming a right triangle XYZ.

Step 2: Apply the Pythagorean theorem. Since triangle XYZ is a right triangle, the square of the length of the hypotenuse (XY) is equal to the sum of the squares of the lengths of the other two sides (XZ and ZY).

Step 3: Use the properties of circles. The length of XZ is the sum of the radii of the circles with centers X and Z, or 9 cm + r cm. The length of ZY is the sum of the radii of the circles with centers Z and Y, or r cm + 2 cm.

Step 4: Substitute these lengths into the Pythagorean theorem. (9 cm + r cm)^2 + (r cm + 2 cm)^2 = (17 cm)^2.

Step 5: Solve for r. This is a quadratic equation in r, which can be solved by factoring, completing the square, or using the quadratic formula. The solution is r = 6 cm.

So, the correct choice is 6 cm.

Knowee AI · Accepted Answer

This problem can be solved using the properties of right triangles and the properties of circles.

Step 1: Draw a diagram. Draw two circles with centers X and Y and radii 9 cm and 2 cm respectively. Draw a line segment XY of length 17 cm. Draw a third circle with center Z and radius r cm that touches the other two circles externally. Draw a line segment from X to Z and from Z to Y, forming a right triangle XYZ.

Step 2: Apply the Pythagorean theorem. Since triangle XYZ is a right triangle, the square of the length of the hypotenuse (XY) is equal to the sum of the squares of the lengths of the other two sides (XZ and ZY).

Step 3: Use the properties of circles. The length of XZ is the sum of the radii of the circles with centers X and Z, or 9 cm + r cm. The length of ZY is the sum of the radii of the circles with centers Z and Y, or r cm + 2 cm.

Step 4: Substitute these lengths into the Pythagorean theorem. (9 cm + r cm)^2 + (r cm + 2 cm)^2 = (17 cm)^2.

Step 5: Solve for r. This is a quadratic equation in r, which can be solved by factoring, completing the square, or using the quadratic formula. The solution is r = 6 cm.

So, the correct choice is 6 cm.

X and Y are centres of circles of radii 9 cm and 2 cm respectively, XY = 17 cm. Z is the centre of a circle of radius r cm which touches the above circles externally. Given that angle(XZY) = 90 deg, the value of r isChoices:- 6 CM 8 CM 9 CM 13 CM

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