Construct a direct common tangent to two circles of radii 4 cm and 2 cm whose centers are 8 cm apart. Measure and verify the length of the tangent.

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

7.75 cm

5.75 cm

7.70 cm

2.75 cm

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given,
Circle C1 with radius

r_{1}

= 4 cm center A
Circle C2 with radius

r_{2}

= 2 cm center B
Distance between center d= 8 cm
So length of tangent,

PQ = \sqrt{d^{2} - {(r_{1} - r_{2})}^{2}}

PQ = \sqrt{8^{2} - {(4 - 2)}^{2}}

PQ = \sqrt{8^{2} - 2^{2}}

PQ = 7.75 cm

Now, make a line AB with measure of 8 cm.
From point A make a circle C1 of radius 4 cm with center A.
From point B make a circle C2 of radius 2 cm with center B.
From point A make another circle C3 of radius (4-2)=2 cm with center A.
Now from the midpoint of AB, M draw another circle C4 with radius 4 cm.
At point where circle C4 cuts C3, E and F join them with A to make AE and AF
Here extent AE and AF to P and R respectively to meet C1.
Make,
BQ∥AP and BS∥AR
Join P to Q and R to S
So, we get
Direct tangents = PQ and RS.
Question Image