# Out of the two co

Let C1 and C2 are two concentric circles with center O and radius of outer circle is 5 cm.

Given : AC is a chord with length 8 cm that is tangent to inner circle .

To find : Radius of inner circle i.e. OD

AC is a tangent for C1 at D so,

OD AC [Tangent at a point on the circle is perpendicular to the radius through point of contact ]

So, OAD is a right-angled triangle at D .

Also it implies that OD is perpendicular to the chord AC in C2

So we have,

AD = DC [perpendicular from the center to the chord bisects the chord]

(5)2 = (OD)2+ (4)2

25 = (OD)2 + 16

(OD)2= 9

OD = 3 cm

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Area Related to Circles- Important Formula and Concepts59 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses