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