Suppose C and D are centres of two circles of radii 16 cm and 9 cm respectively, and distance between the centres is 25 cm. Find the length of direct common tangent.
24 cm
Length of the direct common tangent = \(\sqrt{d^2 - (r_1 - r_2)^2}\), where d is the distance between the centres.
Here d = 25 cm, \(r_1 = 16\) cm and \(r_2 = 9\) cm, so \(r_1 - r_2 = 7\) cm.
Length = \(\sqrt{25^2 - 7^2} = \sqrt{625 - 49} = \sqrt{576} = 24\) cm.
Check: 7, 24 and 25 form a Pythagorean triple (49 + 576 = 625), confirming the right triangle formed by the tangent, the radius difference and the line of centres.
Hence, 24 cm.
Similar Questions
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Important Questions from Circles, Chords and Tangents
AB is a chord of a circle with centre O and P is any point on the circle. If ∠APB = 112°, then what is the measure of ∠OAB ?
The distance between the centres of two circles is 24 cm. If the radius of the two circles are 4 cm and 8 cm, then what is the sum of the lengths (in cm) of the direct common tangent and the transverse common tangent?
An equilateral triangle ABC and a scalene triangle DBC are inscribed in a circle on same side of the arc. what is ∠BDC equal to?
What can be the maximum number of common tangent which can be drawn to two non-intersecting circles?
There are two identical circles of radius 10 cm each. If the length of the direct common tangent is 26 cm, then what is the length (in cm) of the transverse common tangent?
