Question

construct two circles of radii 4 cm and 2cm . whose are 8cm apart construct a tanserve common tangent means and write its length
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Answer 1

Given : two circles of radii 4 cm and 2cm . whose center are 8cm apart  

To find : Construct Circle &  a tanserve common tangent

Solution:

Step 1 :   Draw a  line Segment AB = 8 cm

Step 2 : Draw a circle Taking A as center & Compass width = 2 cm  

Step 3 : Draw a circle Taking B  as center & Compass width = 4 cm  

Step 4 : Extend BA  

Step 5 : Taking Compass width = AB  & taking A as center Draw a Semicircle Such that it intersect Extended BA  at P   &    circle of radius 4 cm at  R

Step 6 : join PR , touching 2 cm Radius circle at Q

PQR  is Common Tangent

Length   PQ = 2√15    PR =  4√15  & QR = 2√15

PR ≈ 15.5 cm

Mathematical

(8 /16) = (2/4)  = 2√15/ 4√15    = 1/2

√(8² - 2²) = √64 - 4  = √60 = 2√15

& √(16² - 4²) = √256 - 16  = √240 = 4√15

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