Advertisements
Advertisements
प्रश्न
In the following figure, ∠OAB = 30º and ∠OCB = 57º. Find ∠BOC and ∠AOC.
Advertisements
उत्तर
Given, ∠OAB = 30° and ∠OCB = 57°
In ΔAOB, AO = OB ...[Both are the radius of a circle]
⇒ ∠OBA = ∠BAO = 30° ...[Angles opposite to equal sides are equal]
In ΔAOB,
⇒ ∠AOB + ∠OBA + ∠BAO = 180° ...[By angle sum property of a triangle]
∴ ∠AOB + 30° + 30° = 180°
∴ ∠AOB = 180° – 2(30°)
= 180° – 60°
= 120° ...(i)
Now, in ΔAOB,
OC = OB ...[Both are the radius of a circle]
⇒ ∠OBC = ∠OCB = 57° ...[Angles opposite to equal sides are equal]
In ΔOCB,
∠COB + ∠OCB + ∠CBO = 180° ...[By angle sum property of triangle]
∴ ∠COB = 180° – (∠OCB + ∠OBC)
= 180° – (57° + 57°)
= 180° – 114°
= 66° ...(ii)
From equation (i), ∠AOB = 120°
⇒ ∠AOC + ∠COB = 120°
⇒ ∠AOC + 66° = 120° ...[From equation (ii)]
∴ ∠AOC = 120° – 66° = 54°
APPEARS IN
संबंधित प्रश्न
PA and PB are tangents from P to the circle with centre O. At point M, a tangent is drawn cutting PA at K and PB at N. Prove that KN = AK + BN.
In the fig two tangents AB and AC are drawn to a circle O such that ∠BAC = 120°. Prove that OA = 2AB.
Fill in the blank:
A point whose distance from the centre of a circle is greater than its radius lies in ..................... of the circle.
In the given figure, a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D, are of lengths 4 cm and 3 cm respectively. If the area of ΔABC = 21 cm2 then find the lengths of sides AB and AC.
In the given figure, two tangents RQ and RP are drawn from an external point R to the circle with centre O. If ∠PRQ = 120°, then prove that OR = PR + RQ.
In the given figure, ΔPQR is an isosceles triangle with PQ = PR and m ∠PQR = 35°. Find m ∠QSR and m ∠QTR.
A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. AP and AQ are the tangents to the circle at P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, find the perimeter of the ∆ABC.
Find the length of the chord of a circle in the following when:
Radius is 1. 7cm and the distance from the centre is 1.5 cm
In the given figure, O is the centre of a circle, chord PQ ≅ chord RS If ∠ POR = 70° and (arc RS) = 80°, find –
(1) m(arc PR)
(2) m(arc QS)
(3) m(arc QSR)
Say true or false:
Two diameters of a circle will necessarily intersect.
