Question

Diameters of two concentric circles are a and
b. (b> a) and its measurement is c. Prove that
b2 = a²+c²​

Answer 1

Answer:

Given: d1, d2 (d2 > d1) be the diameters of two concentric circles and C be the lengths of a chord of a circle which is tangent to the other circle.

To prove : d22 = d12 + c2

Since OQ and OR are radii of two circles with diameters d2 and d1 respectively,therefore,OQ=d22,OR=d12 and PQ = c.

Since PQ is the tangent to the circle,

therefore, OR is perpendicular to PQ.

⇒QR=PQ2=c2

Using Pythagoras theorem in ΔOQR, we have

OQ2 = QR2 + QR2

⇒(d22)2=(d12)2+(c2)2

⇒14(d2)2=14(d1)2+(c)2

⇒d22=d21+c2

Hence proved.