Advertisements
Advertisements
प्रश्न
In the below fig. O is the centre of the circle. If ∠APB = 50°, find ∠AOB and ∠OAB.
Advertisements
उत्तर
ΔAPB = 50°
By degree measure theorem
∠AOB=2 ∠APB
⇒∠APB= 2 × 50° = 100°
Since OA =OB
[ Radius of circle ]
Then ∠OAB=∠OBA
[ Angle's opposite to equal sides ]
Let ∠OAB = x
In Δ OAB by angle sum property
`∠OAB+∠OBA+∠AOB=180°`
`⇒x+x+100=180°`
`⇒2x+100=180°`
`⇒2x=80°`
`⇒x=40°`
`∠OAB =∠OBA= 40°`
APPEARS IN
संबंधित प्रश्न
In figure OQ : PQ = 3 : 4 and perimeter of ΔPDQ = 60cm. determine PQ, QR and OP.
In Fig. 1, the sides AB, BC and CA of a triangle ABC, touch a circle at P, Q and R respectively. If PA = 4 cm, BP = 3 cm and AC = 11 cm, then the length of BC (in cm) is ?
In the given figure, BDC is a tangent to the given circle at point D such that BD = 30 cm and CD = 7 cm. The other tangents BE and CF are drawn respectively from B and C to the circle and meet when produced at A making BAC a right angle triangle. Calculate (i) AF
In the given figure, PO \[\perp\] QO. The tangents to the circle at P and Q intersect at a point T. Prove that PQ and OTare right bisector of each other.
ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm (not drawn to scale). Three circles are drawn touching each other with the vertices as their centres. Find the radii of the three circles.
Use the figure given below to fill in the blank:
Diameter of a circle is ______.
Use the figure given below to fill in the blank:
Tangent to a circle is _______.
Use the figure given below to fill in the blank:
Diameter = 2 x ________
In figure, chords AC and DE intersect at B. If ∠ABE = 108°, m(arc AE) = 95°, find m(arc DC).
A circle of radius 3 cm with centre O and a point L outside the circle is drawn, such that OL = 7 cm. From the point L, construct a pair of tangents to the circle. Justify LM and LN are the two tangents.
