#### Two circles touch externally, if the distance between their centres is equal to the ____ of their radii.

Two circles touch externally, if the distance between their centres is equal to the sum of their radii.

#### The angle subtended by an arc of a circle at the centre is ____ the angle subtended by the same arc at any point on the remaining part of the circle.

The angle subtended by an arc of a circle at the centre is double the angle subtended by the same arc at any point on the remaining part of the circle.

#### The area of a sector of a circle of radius 5 cm formed by an arc of length 3.5 cm is____.

Area of the sector = 1 /2 × l × r = 1 /2 × 3.5 × 5 = 8.75 cm^{2}

#### The diameter of a semi-circular window is 63 cm. Its perimeter = ____.

Perimeter of window = πr + 2r = 22 /7 × 63 /2 + 63 = 99 + 63 = 162 cm Hence, the perimeter of the window is 162 cm.

#### If two chords of a circle are equal, then their corresponding arcs are congruent.

If two chords of a circle are equal, then their corresponding arcs are congruent.

#### If two circles of radii 4 cm and 7 cm touch internally, then the distance between their centres is ____.

Distance between the centres of the circles = Difference of their radii =7−4 =3 cm

#### The perpendicular bisectors of two chords of a circle meet at its centre.

The perpendicular bisectors of two chords of a circle meet at its centre.

#### When two circles touch internally the distance between their centers is equal to ____.

When two circles touch each other internally, the distance between the centres is equal to the difference between their radii.

#### If the angles subtended by chords of a circle at the centre are equal, then the chords are equal.

If the angles subtended by chords of a circle at the centre are equal, then the chords are equal.