A chord of length 8 cm is drawn at a distance of 3 cm from the center of a circle. Calculate the radius of a circle.
The radius of a circle is 17.0 cm and the length of perpendicular is drawn from its center to a chord is 8-0 cm. Calculate the length of the chord.
A chord of length 24 cm is at a distance of 5 cm from the center of the circle. Find the length of the chord of the same circle which is at a distance of 12 cm from the center.
In a circle of radius 17 cm, two parallel chords of lengths 30 cm and 16 cm are drawn. Find the distance between the chords, if both chords are:
(i) On the opposite sides of the center,
(ii) On the same side of the center.
The given figure shows a pentagon ABCDE. EG drawn parallel to DA meets BA produced at G and CF drawn parallel to DB meets AB produced at F.
Prove that the area of pentagon ABCDE is equal to the area of triangle GDF.
The figure given below shows a circle with center O in which diameter AB bisects the chord CD at point E. If CE = ED = 8 cm and EB = 4 cm, find the radius of the circle.
In the given figure, O is the center of the circle. AB and CD are two chords of the circle. OM is perpendicular to AB and ON is perpendicular to CD. AB = 24 cm, OM = 5 cm, ON = 12 cm. Find the:
(i) the radius of the circle.
(ii) length of chord CD.
A straight line is drawn cutting two equal circles and passing through the midpoint M of the line joining their centers O and O’.
Prove that chords AB and CD, which are intercepted by the two circles are equal.
M and N are the mid-points of two equal chords AB and CD respectively of a circle with center O. Prove that:
(i) ∠BMN = ∠DNM,
(ii) ∠AMN = ∠CNM.
In the following figure: P and Q are the points of intersection of two circles with centers O and O’. If straight lines APB and CQD are parallel to OO’. Prove that
(i) OO’ = ½ AB
(ii) AB = CD
Two equal chords AB and CD of a circle with center O, intersect each other at a point P inside the circle. Prove that :
(i) AP = CP
(ii) BP = DP
In the following figure, OABC is a square. A circle is drawn with O as the centre which meets OC at P and OA at Q. Prove that:
(i) △ OPA ≅ △ OQC, (ii) △ BPC ≅ △ BQA.
The length of the common chord of two intersecting circles is 30 cm. If the diameters of these two circles are 50 cm and 34 cm, calculate the distance between their centers.
The line joining the mid-points of two chords of a circle passes through its center. Prove that the chords are parallel.
In the following figure, the line ABCD is perpendicular to PQ; where P and Q are the centers of the circles. Show that
(i) AB = CD, (ii) AC = BD.
In the given figure, an equilateral triangle ABC is inscribed in a circle with center O. Find:
(i) ∠BOC
(ii) ∠OBC
In the given figure, a square is inscribed in a circle with center O. Find:
(ii) ∠OCB
(iii)∠COD
(iv) ∠BOD
Is BD a diameter of the circle?
In the given figure, AB is a side of a regular pentagon and BC is a side of a regular hexagon.
(i) ∠AOB
(ii) ∠BOC
(iii) ∠AOC
(iv) ∠OBA
(v) ∠OBC
(vi) ∠ABC
In the given figure, AB=BC=DC and ∠AOB=50°.
(i) ∠AOC
(ii) ∠AOD
(iii) ∠BOD
(iv) ∠OAC
(v) ∠ODA
In the given figure, O is the center of the circle and the length of arc AB is twice the length of the arc BC. If ∠AOB=100°, find:
(ii) ∠OAC
Draw two circles of different radii. How many points these circles can have in common? What is the maximum number of common points?
In the given figure, AB and CD are two equal chords of a circle, with center O. If P is the the midpoint of chord AB, Q is the midpoint of chord CD and ∠POQ=150°, find ∠APQ.
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