Radii of two circles are 3 cm and 8 cm. The centres of the two circles are 13 cm apart. Find the length of the direct common tangent to the two circles.
Answers
The length of a direct common tangent is 12 cm.
Step-by-step explanation:
Since we have given that
Radii of two circles = 8 cm and 3 cm
Distance between their centres = 13 cm
We need to find the length of a direct common tangent to the two circles.
As we know that
Length D2 – (R – r)²
Length = V132 – (8 3)2
Length = V169 – 52
Length = V169 – 25
Length = V144
Length 12 cm
Answer:
Refer to the attachment for the diagram.
Given:
- OO' = 13 cm
- Radius of circle with center O' = 8 cm
- Radius of circle with center O = 3 cm
Now since the common tangent is parallel to the dotted line, it is enough if we find the value of the dotted line, as both the length of the tangent and dotted line are equal.
Let us assume the length of the dotted line to be 'x' cm.
Now we can see a right angled triangle OAO'. Hence applying Pythagoras Theorem we get:
⇒ O'A² + OA² = O'O²
⇒ 5² + x² = 13²
⇒ 25 + x² = 169
⇒ x² = 169 - 25
⇒ x² = 144
⇒ x = √144 = 12 cm
Hence the length of the dotted line is equal to 12 cm.
Therefore the length of the common tangent is also equal to 12 cm.
