Question

Q.1/10:The distance between the centres of two equal
circles each of radius 8 cm is 34 cm. The length of a
transverse tangent is:

Answer 1

Answer:

Length of Common Tangent is 8 cm

Given:-

Radius of each Circle ,r = 3 cm

Distance between two circle ,d = 10cm

Number of Circle = 2

To Find:-

Length of transverse Common Tangent

Solution:-

As we have to calculate the length of a transverse Common Tangent .

Using Formula

• Length of common tangent = √d² -(r + r)²

Substitute the value we get

→ Length of common tangent = √10² - (3+3)²

→ Length of common tangent = √100 -(6)²

→ Length of common tangent = √100-36

→ Length of common tangent = √64

→ Length of common tangent = 8 cm

Hence, the Length of the common tangent is 8 cm.

For More Information Refer to Attachment !!

Answer 2

Answer:

30cm is the length of the transverse tangent

Explanation:

Given , radius of the given circles is 8cm and the distance between the centres of two equal circles = 34cm.

Let two circle with same radius and let the centres be  X and Y.

Let PQ  be the transverse tangent  of the given  two circle .

Radius of 1st  and 2nd circle = 8 cm

and the distance between the centres of two circles = 34cm .

Step 1:

From the formula ,

$(Length of \ transverse\ tangent) ^{2} = [distance\ between\ the centres})^{2} - (r_{1} +r_{2} )^{2} ]$

According to the formula ,

$(PQ)^{2} = (XY)^{2} - (r_{1} +r_{2} )^{2}$   [$r_{1} and \ r_{2}$ be the radius of the circles]

⇒$(PQ)^{2} = (34)^{2} - (8+8)^{2}$

[XY is the distance between the centres of the circle ]

⇒$(PQ)^{2} = 1156 - 256$

⇒$(PQ)^{2} = 900$

⇒PQ = $\sqrt{900}$ =  30cm

Final answer:

Hence , the length of the transverse tangent is 30cm .

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