Question

4. Circle X has a radius of 4 cm. Which given
measurement would give a circle congruent to
Circle X?
A. Diameter = 7.5 cm B. Diameter = 8 cm
C. Radius = 4.2 cm D. Radius = 8 cm​

Answer 1

★$\huge\bf{\blue{\underline{Question:-}}}$

Circle X has a radius of 4 cm. Which given

measurement would give a circle congruent to

Circle X?

A. Diameter = 7.5 cm B. Diameter = 8 cm

C. Radius = 4.2 cm D. Radius = 8 cm

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★$\huge\bf{\green{\underline{Explanation:-}}}$

(1)Draw two concentric circle C1 and C2 with common center

0 and radius 4cm and 6cm

(2) Take a point P on the outer circle C2 and join OP.

(3) Draw the bisector of OP which bisect OP at M'.

(4) Taking M' as center and OM' as radius draw a dotted circle which

cut the inner circle C1 at two point M and P.

(5) Join PM and PP'.  Thus, PM and PP' are required tangent.

On measuring PM and PP'.

PM=PP′=4.4cmBycalculation:InΔOMP,∠PMO=900PM2=OP2−OM2(bypythagorastheorem)PM2=(6)2−(4)2=36−16=20PM2=20cmPM=20=4.4cmHence,thelengthofthetangentis4.4cm

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Answer 2

(1)Draw two concentric circle C1 and C2 with common center

0 and radius 4cm and 6cm

(2) Take a point P on the outer circle C2 and join OP.

(3) Draw the bisector of OP which bisect OP at M'.

(4) Taking M' as center and OM' as radius draw a dotted circle which

cut the inner circle C1 at two point M and P.

(5) Join PM and PP'. Thus, PM and PP' are required tangent.

On measuring PM and PP'.

PM=PP′=4.4cmBycalculation:InΔOMP,∠PMO=900PM2=OP2−OM2(bypythagorastheorem)PM2=(6)2−(4)2=36−16=20PM2=20cmPM=20=4.4cmHence,thelengthofthetangentis4.4cm

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