R d sharma solutions mathematics class 9 Solutions for Chapter 16 circles

Fill in the blanks:

(i) All points lying inside/outside a circle are called___ points/ points.

(ii) Circles having the same centre and different radii are called_ circles.

(iii) A point whose distance from the center of a circle is greater than its radiuslies in_ of the circle.

(iv) A continuous piece of a circle is_ of the circle.

(v) The longest chord of a circle is a _____of the circle.

(vi) An arc is a_ when its ends are the ends of a diameter.

(vii) Segment of a circle is a region between an arc and _____of the circle.

(viii) A circle divides the plane, on which itlies, in _____parts.

Find the length of a chord which is at a distance of 5 cm from the centre of a circle of radius 10 cm.

Prove that the line joining the mid-point of a chord to the centre of the circle passes through the mid-point of the corresponding minor arc.

A circular park of radius 40 m is situated in a colony. Three boys Ankur, Amit and Anand are sitting at equal distance on its boundary each having a toy telephone in his hands to talk to each other. Find the length of the string of each phone.

In figure, O is the centre of the circle. Find ∠BAC.

If O is the centre of the circle, find the value of x in each of the following figures.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

(xi)

(xii)

O is the circumcentre of the triangle ABC and OD is perpendicular on BC. Prove that ∠BOD = ∠A

In figure, O is the centre of the circle, then prove that ∠x = ∠y + ∠z

If ABCD is a cyclic quadrilateral in which AD||BC (figure). Prove that ∠B = ∠C.

In figure, O is the centre of the circle. Find ∠CBD

In figure, AB and CD are diameters of a circle with centre O. If ∠OBD = 50^0 find ∠AOC.

In a cyclic quadrilateral ABCD if AB||CD and B = 70^0 , find the remaining angles.

In a cyclic quadrilateral ABCD, if m ∠A = 3(m∠C). Find m ∠A.