Advertisements
Advertisements
प्रश्न
AB is a diameter of a circle with centre O and radius OD is perpendicular to AB. If C is any point on arc DB, find ∠ BAD and ∠ ACD.
उत्तर
Since, chord BD makes ∠BOD at the centre and ∠BAD at A.
∴ ∠BAD = `1/2`∠BOD
= `1/2` x 90°
= 45°
Similarly,
Chord AD makes ∠AOD at the centre and ∠ACD at C.
∴ ∠ACD = `1/2`∠AOD
= `1/2` x 90° = 45°
Thus, ∠BAD = ∠ACD = 45°.
APPEARS IN
संबंधित प्रश्न
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 the chords are
(i) on the opposite sides of the centre,
(ii) on the same side of the centre.
In the following figure, a circle is inscribed in the quadrilateral ABCD.
If BC = 38 cm, QB = 27 cm, DC = 25 cm and that AD is perpendicular to DC, find the radius of the circle.
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.
From a point P outside a circle, with centre O, tangents PA and PB are drawn. Prove that:
OP is the ⊥ bisector of chord AB.
In the given figure, M is the centre of the circle. Chords AB and CD are perpendicular to each other.
If ∠MAD = x and ∠BAC = y : express ∠ABD in terms of y.
In the given figure, M is the centre of the circle. Chords AB and CD are perpendicular to each other.
If ∠MAD = x and ∠BAC = y , Prove that : x = y
Two parallel chords are drawn in a circle of diameter 30.0 cm. The length of one chord is 24.0 cm and the distance between the two chords is 21.0 cm;
find the length of another chord.
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.
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 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.
