Ncert Solutions For Class 9 Maths Ex 10.3

Ncert Solutions For Class 9 Maths Chapter 10 Ex 10.3

Exemplar problems

1. If V1 , V2 (V2 > V1) be the diameters of two concentric circles and Z be the length of a chord of a circle which is tangent to the other circle, prove that : V22=Z2+V12.

Solution:-

Let XY be a chord of a circle which touches the other circle at Z. Then ΔOZY is a right triangle.

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∴          By Pythagoras Theorem,

OZ2 + ZY2= OY2

i.e.,        (V12)2+ (Z2)2= (V22)2

           V124+ Z24=            V224

         V22+Z2=V12

 

2. Two tangents AB and AC are drawn from an external point to a circle with centre 0. Prove that BOCA is a cyclic quadrilateral.

Sol. We know that,  tangents to a circle is perpendicular to its radius at the point of contact.

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∴     OCAC and OBAB

OCA=OBA=90

OCA+OBA=90+ 90

=180

Sum of opposite angles of quadrilateral BOCA is 180

Hence, BOCA is a cyclic quadrilateral.