Let A, B be the centres of two circles of equal radii; draw them so that each one of them passes through the centre of the other. Let them intersect at C and D. Examine whether $¯ ¯¯¯¯¯¯ ¯ A B$ and $¯ ¯¯¯¯¯¯¯ ¯ C D$ are at right angles.

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Solution

Draw two circles of equal radii taking A and B as their centre such that one of them passes through the centre of the other.

Since the radii of both the circles are equal, so if one passes through the centre of the other then the later will automatically pass through the centre of the first one.

They intersect at C and D. Join AB and CD. Yes, AB and CD intersect at right angle as $∠ C O B$ is equal to $90^{\circ}$

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¯ ¯¯¯¯¯¯ ¯ A B

and

¯ ¯¯¯¯¯¯¯ ¯ C D

are at right angles.

Question 5

Let A, B be the centres of two circles of equal radii; draw them so that each one of them passes through the centre of the other. Let them intersect at C and D. Examine whether $¯ ¯¯¯¯¯¯ ¯ A B$ and $¯ ¯¯¯¯¯¯¯ ¯ C D$ are at right angles.

AB and CD are two equal chords of a circle with centre O which intersect each other at right angles at point P. If the perpendiculars from the centre to AB and CD meet them at M and N respectively, then MONP is a_______.

AB & CD are two equal chords of a circle with Centre O, which intersect each other at a right angle at point P. If the perpendiculars from the centre to AB and CD meet them at M and N respectively, then MONP is a_______.

In the given figure, AB and CD are equal chords of a circle with centre O. If AB and CD intersect each other at right angle at point P and perpendiculars from the centre to AB and CD meet them at M and N respectively, then MONP is a_______.

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Let A, B be the centres of two circles of equal radii; draw them so that each one of them passes through the centre of the other. Let them intersect at C and D. Examine whether ¯¯¯¯¯¯¯¯AB and ¯¯¯¯¯¯¯¯¯CD are at right angles.

Let A, B be the centres of two circles of equal radii; draw them so that each one of them passes through the centre of the other. Let them intersect at C and D. Examine whether $¯ ¯¯¯¯¯¯ ¯ A B$ and $¯ ¯¯¯¯¯¯¯ ¯ C D$ are at right angles.