Advertisements
Advertisements
प्रश्न
In the given figure, O is the centre of the circle. PQ is a tangent to the circle at T. Chord AB produced meets the tangent at P.
AB = 9 cm, BP = 16 cm, ∠PTB = 50° ∠OBA = 45°
Find:
- Length of PT
- ∠BAT
- ∠BOT
- ∠ABT
उत्तर
a.
PT2 = AP × BP
= (AB + BP) × BP
= (9 + 16) × 16
= 25 × 16
= 400
∴ PT = `sqrt(400)`
= 20 cm
b. Angles in alternate segments are equal
∴ ∠BAT = ∠PTB
= 50°
c. OT ⊥ PQ
∴ ∠OTP = 90°
`\implies` ∠OTP + ∠PTB = 90°
`\implies` ∠OTB + ∠50° = 90°
`\implies` ∠OTB = 90° – 50° = 40°
Now, In ΔBOT,
OB = OT(Radii of same circle)
∠OTB = ∠OBT = 40°
and ∠BOT + ∠OTB + ∠OBT = 180°
∠BOT + 40° + 40° = 180°
∠BOT = 180° – 80°
= 100°
d. In ΔABT,
∠ABT = ∠OBA + ∠OBT
= 45° + 40°
= 85°
APPEARS IN
संबंधित प्रश्न
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is ______.
In the given figure, PA and PB are tangents to the circle from an external point P. CD is another tangent touching the circle at Q. If PA = 12 cm, QC = QD = 3 cm, then find PC + PD
In the given figure O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC = 7.5 cm. Calculate the radius of a circle.
In the given figure O is the centre of the circle. Tangents A and B meet at C. If ∠ACO = 30°, find
1) ∠BCO
2) ∠AOB
3) ∠APB
How many common tangents can be drawn to two circles, touching each
other externally?
The length of the direct common tangent to two circles of radii 12cm and 4cm is 15cm. calculate the distance between their centres.
In the given figure, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD = 7.8 cm, PD = 5 cm, PB = 4 cm. Find AB.
In figure, M is the centre of the circle and seg KL is a tangent segment. If MK = 12, KL = `6sqrt(3)`, then find
(i) Radius of the circle.
(ii) Measures of ∠K and ∠M.
At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A is ______
Assertion (A): A tangent to a circle is perpendicular to the radius through the point of contact.
Reason (R): The lengths of tangents drawn from an external point to a circle are equal.
