Question

4. The two tangents drawn from an external point P to a circle with centre O are perpendicular to each other. If length of each tangent is 6 cm, then radius of the circle is А. 3cm
B. 6cm
C. 9cm
D. 12cm​

Answer 1

Answer:

(B)

Step-by-step explanation:

6cm (B)

Answer 2

Given : The two tangents drawn from an external point P to a circle with centre O are perpendicular to each other.

Length of each tangent is 6 cm,  

To Find :

Radius of the circle  

А. 3cm

B. 6cm

C. 9cm

D. 12cm​

Solution:

Let say Tangents are PA and PB

PA = PB = 6 cm

OA = OB = Radius = R cm

OAPB  is  a  Quadrilateral

∠OAP = ∠OBP = 90°   Tangents

∠APB = 90°   Given

Sum of all the angles of  Quadrilateral is 360°

Hence remaining angle ∠AOB is also 90°

as PA = PB = 6 cm ( adjacent sides are equal )

Hence OAPB  is  Square

OA = OB = PA = PB = 6 cm

=> Radius = 6 cm

Correct option is B)  6 cm

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