Question

the sum of the radii of two concentric circles is 8cm and difference of their areas is 16πcmsq
a) form the pair of linear equation for the above statement​

Answer 1

Answer:

Step-by-step explanation:

OD of smaller circle = 8cm.

EB is tangent to the inner circle at point D. So, OD is perpendicular to EB.( as tangent is perpendicular to the radius segment through the point of contact.)

Construction: Join AD & Join AE.

PROOF: In right triangle ODB

DB² = OB² — OD² ( by pythagoras law)

DB² = 13² — 8² = 169 — 64 = 105

=> DB = √105

=> ED = √105 ( as perpendicular OD from the centre of the circle O, to a chord EB , bisects the chord)

Now in triangle AEB, angle AEB = 90°( as angle on a semi circle is a right angle).

And,...(more)

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Ashish Gupta

Ashish Gupta, Mathematics is my game

Answered Feb 28, 2016

Given OD=8cm

         OB=13cm

Firstly find DB.

Using Pythagoras Theorem, DB^2=OB^2 - OD^2. This gives DB = sqrt(105) = DE.