Advertisements
Advertisements
प्रश्न
In figure, AT is a tangent to the circle with centre O such that OT = 4 cm and ∠OTA = 30°. Then AT is equal to ______.
पर्याय
4 cm
2 cm
`2sqrt3` cm
`4sqrt3` cm
उत्तर
In figure, AT is a tangent to the circle with centre O such that OT = 4 cm and ∠OTA = 30°. Then AT is equal to `underlinebb(2sqrt(3) cm)`.
Explanation:
∠OAT = 30° ...[∵ Tangent and radius are ⊥ to each other at the point of contact]
In right-angled ΔOAT,
`"AT"/"OT"` = cos 30°
⇒ `sqrt3/2="AT"/4`
⇒ `"AT" = (sqrt3xx4)/2`
⇒ AT = `2sqrt3` cm.
APPEARS IN
संबंधित प्रश्न
If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is 60°, then find the length of OP
In the given Figure, AB and AC are tangents to the circle with centre O such that ∠BAC = 40°. Then ∠BOC is equal to ______
Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc.
A chord of a length 16.8 cm is at a distance of 11.2 cm from the centre of a circle . Find the length of the chord of the same circle which is at a distance of 8.4 cm from the centre.
ABCD is a cyclic quadrilateral PQ is a tangent at B. If ∠DBQ = 65°, then ∠BCD is ______
The distance between the centres of equal circles each of radius 3 cm is 10 cm. The length of a transverse tangent AB is ______
Construct a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.
If O is centre of a circle and Chord PQ makes an angle 50° with the tangent PR at the point of contact P, then the angle subtended by the chord at the centre is ______.
In the given figure, AB and AC are tangents to the circle. If ∠ABC = 42°, then the measure of ∠BAC is ______.
In the given figure, QR is a common tangent to the two given circles touching externally at A. The tangent at A meets QR at P. If AP = 4.2 cm, then the length of QR is ______.
