Draw two concentric circles of radii 3cm and 5cm. From a point on the outer circle, construct a pair of tangents to the inner circle. Measure their lengths and verify the measurement by actual calculation.??

Step 1

Take a point O and draw two concentric circles of radii 3 cm and 5 cm respectively.

Step 2

Locate a point P on the circumference of larger circle.

Step 3

Join OP and bisect it . Let M be the midpoint of OP.

Step 4

Taking M as centre and MP(or MO) as radius,draw a circle intersecting smaller circle at A and B.

Step 5

Join PA and PB .Thus PA and PB are the required tangents.

Now after measuring PA and PB comes out to be 4 cm

Verification of measurement by actual calculation:-

Join OA

$Nowin\u2206POA\phantom{\rule{0ex}{0ex}}SincePAisa\mathrm{tan}genttothecirclesoOA\perp AP.\phantom{\rule{0ex}{0ex}}ThusPOAisarightangledtriangle\phantom{\rule{0ex}{0ex}}U\mathrm{sin}gpythagorastheorem\phantom{\rule{0ex}{0ex}}P{A}^{2}+O{A}^{2}=O{P}^{2}\phantom{\rule{0ex}{0ex}}\Rightarrow P{A}^{2}=O{P}^{2}-O{A}^{2}\phantom{\rule{0ex}{0ex}}\Rightarrow P{A}^{2}=(5cm{)}^{2}-(3cm{)}^{2}\phantom{\rule{0ex}{0ex}}\Rightarrow P{A}^{2}=16c{m}^{2}\phantom{\rule{0ex}{0ex}}\Rightarrow PA=4cmthusverified\phantom{\rule{0ex}{0ex}}$

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