In the given figure O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC =7.5 cm, find the radius of the circle.

Open in App

Solution

Let the radius of the circle be ‘r’ CD = 2r (given, CD is diameter of the circle) AB is tangent to the circle (given)

$∴ A B^{2} = A C \times A D$

$(15)^{2} = 7.5 (7.5 + 2 r)$ ( 1 mark)

$15 \times 15 = \frac{75}{10} (7.5 + 2 r)$

$15 \times 15 = \frac{75}{10} (7.5 + 2 r)$

$30 = 7.5 + 2 r$

$22.5 = 2 r$

$r = 11.25 c m$ ( 1 mark)

Suggest Corrections

Similar questions

Q. In the given figure, AB and AC are tangents to a circle with centre O and radius 8 cm. If OA = 17 cm, then the length of AC (in cm) is
(a) 9 cm
(b) 15 cm
(c)

\sqrt{353}

cm
(d) 25 cm

Q. In the given figure, AP, AQ and BC are tangents to the circle. If AB = 5 cm, AC = 6 cm and BC = 4 cm then the length of AP is [CBSE 2012]
(a) 15 cm
(b) 10 cm
(c) 9 cm
(d) 7.5 cm

In the given figure, CD is the diameter of a circle with centre O and CD is perpendicular to chord AB. If AB = 12 cm and CE = 3 cm then radius of the circle is

(a) 6 cm

(b) 9 cm

(d) 8 cm

Q. In the given figure

O

is the centre of the circle and

A B

is a tangent at

B

. If

A B = 15 c m

and

A C = 7.5 c m

. Calculate the radius of the circle.

Q. In the given figure 'O' is the centre of the circle and AB is tangent at B. If AB = 15 cm and AC = 7.5 cm. Calculate the diameter of the circle (in cm). [2 marks]

Join BYJU'S Learning Program

In the given figure O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC =7.5 cm, find the radius of the circle.

Let the radius of the circle be ‘r’ CD = 2r (given, CD is diameter of the circle) AB is tangent to the circle (given) ∴AB2=AC×AD (15)2=7.5(7.5+2r) ( 1 mark) 15×15=7510(7.5+2r) 15×15=7510(7.5+2r) 30=7.5+2r 22.5=2r r=11.25 cm ( 1 mark)