Q5 of 59 Page 58

In fig 3.28 the circles with centres A and B touch each other at E. Line is a common tangent which touches the circles at C and D respectively. Find the length of seg CD if the radii Fig. 3.28 of the circles are 4 cm, 6 cm.



Given that two circles with centre A and B touch each other externally. We know that if the circles touch each other externally, distance between their centres is equal to the sum of their radii.


⇒AB = (4 + 6) cm = 10 cm


In ∆ABC right-angles at A,


BC2 = CA2 + AB2 {Using Pythagoras theorem}


⇒BC2 = 42 + 102


⇒BC2 = 16 + 100


⇒ BC = √116 cm


In ∆DBC,


∠ BDC = 90° because D is the point of contact of tangent CD to circle centred B


BC2 = CD2 + DB2 {Using Pythagoras theorem}


⇒CD2 = 116 - 62


⇒CD2 = 116 - 36


⇒ CD = √80 cm = 4√5


More from this chapter

All 59 →
3

If radii of two circles are 4 cm and 2.8 cm. Draw figure of these circles touching each other –

(i) externally


(ii) internally.


 4

In fig 3.27, the circles with centres P and Q touch each other at R. A line passing through R meets the circles at A and B respectively. Prove that -

(1) seg AP || seg BQ,


(2) ∆ APR ~ ∆ RQB, and


(3) Find ∠ RQB if ∠ PAR = 35°



 1

In figure 3.37, points G, D, E, F are concyclic points of a circle with centre C.

∠ ECF = 70°, m(arc DGF) = 200° find m(arc DE) and m(arc DEF).



 2

In fig 3.38 ∆ QRS is an equilateral triangle. Prove that,

(1) arc RS ≅ arc QS ≅ arc QR


(2) m(arc QRS) = 240°.