Mathematics
The length of the direct common tangent to two circles of radii 12 cm and 4 cm is 15 cm. Calculate the distance between their centres.
Circles
30 Likes
Answer
Let there be two circles with center A and B and radius 12 and 4 cm respectively.
From figure,
TT' is the common tangent.
DT = BT' = 4 cm.
DB = TT' = 15 cm.
In right angled triangle ADB
AD = AT - DT = 12 - 4 = 8 cm
Hence, the distance between two centres = 17 cm.
Answered By
18 Likes
Related Questions
In the figure (i) given below, AB = 8 cm and M is mid-point of AB. Semicircles are drawn on AB, AM and MB as diameters. A circle with centre C touches all three semicircles as shown, find its radius.
In the figure (ii) given below, equal circles with centres O and O' touch each other at X. OO' is produced to meet a circle O' at A. AC is tangent to the circle whose centre is O. O'D is perpendicular to AC. Find the value of
(i)
(ii)
In the given figure, AC is a transverse common tangent to two circles with centres P and Q and of radii 6 cm and 3 cm respectively. Given that AB = 8 cm, calculate PQ.
Calculate the length of a direct common tangent to two circles of radii 3 cm and 8 cm with their centres 13 cm apart.