Question

construct a tangent to a circle of radius 3 cm from a point on the concentric circle radius 5 cm and measure it's length also verify the measurement by actual calculation​

Answer 1

Correct option is

B

4cm,verified

Toconstruct−

twoconcentriccircleswithradii3cm&5cm

andtodrawatangentfromapointAonthe

circumferenceoftheoutercirletotheinnercircle.

Alsotomeasurethelengthofthistangent

andjustifytheresultbycalculation.

Construction−

(I)TakingOascentreandradii3cm&5cm,

twoconcentriccirclesaredrawn.

(II)WetakeanypointAonthecircumferenceof

theoutercircleandjoinAO.

(III)TakingAOasdiameter,asemicircleAPBisdrawn

onAO.

ThesemicircleAPBintersectstheinnercircleatP.

(IV)APisjoined.

(V)APismeasured.

AP=4cm.

Justification−

OPisaradiusofthegiveninnercircleanditisan

angleinthesemicircleAPB.

∴∠OAP=90  

o

⟹OP⊥AP.

Nowweknowthatheradius,throughthepointof

contactofatangenttoacircle,isperpendicularto

thetangent.

∴APisatangenttothegiveninnercircle.

∴APistherequiredtangent.

AgainΔOAPisarightonewithOAashypotenusesince

∠OAP=90  

o

.

So,byPythagorastheorem,

AP=  

OA  

2

−OP  

2

 

​  

=  

5  

2

−3  

2

 

​  

cm=4cm.

So,thelengthofthetangent

=AP=4cmbyactualmeasurement

aswellasbylogicalarguments.

Ans−OptionB.