Mathematics
Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.
Constructions
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Answer
Steps of Construction :
Draw two concentric circles of radii 4 cm and 6 cm with point O as their centre.
Let P be a point on the outer circle. Join OP and draw its perpendicular bisector to meet OP at M.
Taking M as centre and OM (or MP) as radius, draw a circle. Let the circle intersect the smaller circle i.e. circle of radius 4 cm at points A and B.
Join PA and PB. Then PA and PB are the required tangents. On measuring, PA (or PB), we find that PA = 4.5 cm.
Calculation of length of PA
Join OA
In △OAP, ∠OAP = 90° (As angle in semicircle = 90°.)
By pythagoras theorem we get,
OA2 + PA2 = OP2
⇒ PA2 = OP2 - OA2
⇒ PA2 = 62 - 42 = 36 - 16 = 20 cm.
PA = = 4.5 cm.
Hence, the length of tangent = 4.5 cm.
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