Ex.11.2 Q5 Constructions Solution - NCERT Maths Class 10

Go back to  'Ex.11.2'

Question

Draw a line segment \(AB\) of length \(8 \,\rm{cm}\). Taking \(A\) as centre, draw a circle of radius \(4 \,\rm{cm}\) and taking \(B\) as center, draw another circle of radius \(3 \,\rm{cm}\). Construct tangent to each circle from the center of the other circle.

 

Text Solution

 

Steps:

Steps of construction:

(i) Draw \(\begin{align}\rm{AB}=8\, \rm{cm}\end{align}\).With \(A\) and \(B\) as centers \(4 \,\rm{cm}\) and \(3 \,\rm{cm}\) as radius respectively draw two circles.

(ii)  Draw the perpendicular bisector of \(AB\), intersecting \(AB\) at \(O\).

(iii) With \(O\) as center and \(OA\) as radius draw a circle which intersects the two circles at \(P\), \(Q\), \(R\) and \(S\).

(iv) Join \(BP\), \(BQ\), \(AR\) and \(AS\).

(v) \(BP\) and \(BQ\) are the tangents from \(B\) to the circle with center \(A\)\(AR\) and \(AS\) are the tangents from \(A\) to the circle with center \(B\).

 Proof:

\(\angle {APB}=\angle {AQB}=90^{\circ}\) (Angle in a semi-circle)

\(\therefore \rm{AP} \perp \rm{PB}\) and \({AQ} \perp {QB}\)

Therefore, \(BP\) and \(BQ\) are the tangents to the circle with center \(A\).

Similarly, \(AR\) and \(AS\) are the tangents to the circle with center \(B\).

  
Learn math from the experts and clarify doubts instantly

  • Instant doubt clearing (live one on one)
  • Learn from India’s best math teachers
  • Completely personalized curriculum