Advertisements
Advertisements
प्रश्न
In Fig. O is the centre of the circle with radius 5 cm. OP⊥ AB, OQ ⊥ CD, AB || CD, AB = 8 cm and CD = 6 cm. Determine PQ.
उत्तर
Join OA and OC.
Since the perpendicular from the centre of the circle to a chord bisects the chord. Therefore, P and Q are midpoints of AB and CD respectively.
Consequently, AP = PB = `1/2"AB"` = 3 cm.
and CQ = QD = `1/2`CD = 4 cm
In right triangles OAP and OCQ, we have
OA2 = OP2 + AP2 and OC2 = OQ2 + CQ2
⇒ 52 = OP2 + 32 and 52 = OQ2 + 42
⇒ OP2 = 52 - 32 and OQ2 = 52 - 42
⇒ OP2 = 16 and OQ2 = 9
⇒ OP = 4 and OQ = 3
∴ PQ = OP + OQ = (4 + 3) cm = 7 cm.
APPEARS IN
संबंधित प्रश्न
A chord of length 24 cm is at a distance of 5 cm from the centre of the circle. Find the length of the chord of the same circle which is at a distance of 12 cm from the centre.
In the following figure, the line ABCD is perpendicular to PQ; where P and Q are the centres of
the circles. Show that:
(i) AB = CD,
(ii) AC = BD.
Two chords AB and AC of a circle are equal. Prove that the centre of the circle lies on the bisector of angle BAC.
From a point P outside a circle, with centre O. tangents PA and PB are drawn as following fig., Prove that ∠ AOP = ∠ BOP and OP is the perpendicular bisector of AB.
A chord of length 8 cm is drawn at a distance of 3 cm from the center of the circle.
Calculate the radius of the circle.
The figure shows two concentric circles and AD is a chord of a larger circle.
Prove that: AB = CD.
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 given figure, O is the center of the circle with radius 20 cm and OD is perpendicular to AB. If AB = 32 cm,
find the length of CD.
In a circle of radius 10 cm, AB and CD are two parallel chords of lengths 16 cm and 12 cm respectively.
Calculate the distance between the chords, if they are on:
(i) the same side of the center.
(ii) the opposite sides of the center.
In the figure given below, O is the centre 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) radius of the circle
(ii) length of chord CD.
