Tangent is perpendicular to the radius: tangent, radius and distance to the centre by Pythagoras
This type of question, asked 13 times: 20 Jul 2023 S1, 20 Jul 2023 S3, 12 Sep 2024 S2, 13 Sep 2024 S2, 23 Sep 2024 S3, 26 Sep 2024 S1, 17 Sep 2025 S3, 18 Sep 2025 S2, 19 Sep 2025 S1, 19 Sep 2025 S3, 23 Sep 2025 S2, 24 Sep 2025 S1, 24 Sep 2025 S2. All 13 questions below, oldest first.
Try each one first, then open its answer.
Question 1
20 Jul 2023 S1
69PT is a tangent to a circle whose centre is O, and where T is a point on the circle. If PT = 12 cm and PO = 13 cm, then find the radius of the circle.Tap an option to check your answer.
Question 2
20 Jul 2023 S3
51From a point Q, the length of the tangent to a circle is 20 cm and the distance of Q from the centre of the circle is 25 cm. The radius of the circle is:Tap an option to check your answer.
Question 3
12 Sep 2024 S2
68From a point T, the length of the tangent to a circle is 32 cm and the distance of T from the centre is 40 cm. The diameter (in cm) of the circle is:Tap an option to check your answer.
Question 4
13 Sep 2024 S2
57The radius of the circle is 8 cm. The distance of a point lying outside the circle from the centre is 17 cm. The length of the tangent drawn from the outside point to the circle is:Tap an option to check your answer.
Question 5
23 Sep 2024 S3
73The length of the tangent drawn from a point 10 cm away from the centre of a circle with radius 4 cm, is:Tap an option to check your answer.
Question 6
26 Sep 2024 S1
68From a point A, which is at a distance of 17 cm from the centre C of a circle with radius 8 cm, the pair of tangents AB and AD to the circle are drawn. The area of the quadrilateral ABCD is _____ .Tap an option to check your answer.
Question 7
17 Sep 2025 S3
73A tangent line PA is drawn from an external point P to a circle. If the radius is 8 cm and the distance from P to the center is 17 cm, what is the length of the tangent PA?Tap an option to check your answer.
Question 8
18 Sep 2025 S2
73A circle has radius 7 cm. A tangent is drawn from an external point P. If the length of the tangent is 24 cm, what is the distance from P to the center of the circle?Tap an option to check your answer.
Question 9
19 Sep 2025 S1
73The length of each of two tangents drawn from an external point to a circle is 10 cm. What is the approximate distance from the external point to the center of the circle, if the radius is 6 cm?Tap an option to check your answer.
Question 10
19 Sep 2025 S3
69A point P is 13 cm away from the center of a circle. A tangent is drawn from P to the circle, and its length is 12 cm. What is the area of the circle?Tap an option to check your answer.
Question 11
23 Sep 2025 S2
75A point P is outside a circle. The length of the tangent from P is 10 cm, and the distance from P to the center is cm. What is the radius of the circle?Tap an option to check your answer.
Question 12
24 Sep 2025 S1
75A tangent is drawn from a point 17 cm from the center of a circle of radius 8 cm. Find the length of the tangent.Tap an option to check your answer.
Question 13
24 Sep 2025 S2
75A line is drawn from a point P located 13 cm away from the center O of a circle with radius 5 cm. If the line is tangent to the circle, what is the length of the tangent from point P to the point of contact with the circle?Tap an option to check your answer.