Direct common tangent of two separate circles, square of length = d squared - (r1 - r2) squared: find length, distance or a radius
This type of question, asked 10 times: 17 Jul 2023 S3, 19 Jul 2023 S4, 27 Jul 2023 S2, 9 Sep 2024 S1, 17 Sep 2024 S2, 23 Sep 2024 S1, 15 Sep 2025 S1, 18 Sep 2025 S3, 19 Sep 2025 S2, 23 Sep 2025 S3. All 10 questions below, oldest first.
Try each one first, then open its answer.
Question 1
17 Jul 2023 S3
64The distance between the centres of two circles having radii 16 cm and 8 cm, is 26 cm. The length (in cm) of the direct common tangent of the two circles is:Tap an option to check your answer.
Question 2
19 Jul 2023 S4
73The distance between the centres of two circles of radii 2 cm and 6 cm is 5 cm. Find the length of the direct common tangent.Tap an option to check your answer.
Question 3
27 Jul 2023 S2
72The distance between the centres of two circles having radii 22 cm and 18 cm, is 32 cm. The length (in cm) of the direct common tangent of the two circles is :Tap an option to check your answer.
Question 4
9 Sep 2024 S1
67The distance between the centres of two circles of radii cm and cm is cm. If the points of contact of a direct common tangent to these circles are M and Q, then find the length of the line segment MQ.Tap an option to check your answer.
Question 5
17 Sep 2024 S2
54M and N are, respectively, the centres of two circles of radii 12 cm and 8 cm. QR is the common tangent to the circles. If MN = 16 cm, then what will be the length of QR?Tap an option to check your answer.
Question 6
23 Sep 2024 S1
61For two circles of radius 7 units and units, whose centres are 15 units apart, what is the length of the direct common tangent in units? (Correct to 3 decimal places.)Tap an option to check your answer.
Question 7
15 Sep 2025 S1
72Two circles have radii of 12 cm and 4 cm. If the length of a direct common tangent is 15 cm, what is the distance between their centers?Tap an option to check your answer.
Question 8
18 Sep 2025 S3
70Two circles have radii in the ratio . The length of a direct common tangent is , and the distance between their centers is . What is the radius of the smaller circle?Tap an option to check your answer.
Question 9
19 Sep 2025 S2
70Two circles, with radii of and respectively, have their centers separated by a distance of . If the length of a direct common tangent is equal to the distance between the centers, which of the following is true?Tap an option to check your answer.
Question 10
23 Sep 2025 S3
71Two circles have radii of 8 cm and 3 cm. The distance between their centers is 15 cm. What is the length of a direct common tangent?Tap an option to check your answer.