Advertisements
Advertisements
Question
In Fig. AT is a tangent to the circle. If m∠ABC = 50°, AC = BC, Find ∠BAT.
Solution
AC = BC
⇒ ∠CBA = ∠CAB
⇒ ∠CAB = 50°
∴ ∠ACB = 180° - (50° + 50°) = 80°
Now, ∠BAT = ∠BCA ....(Angles are in alternate segments)
⇒ ∠BAT = 80°.
APPEARS IN
RELATED QUESTIONS
In the following figure; If AB = AC then prove that BQ = CQ.
If PQ is a tangent to the circle at R; calculate:
- ∠PRS,
- ∠ROT.
Given O is the centre of the circle and angle TRQ = 30°.
AB is the diameter and AC is a chord of a circle with centre O such that angle BAC = 30°. The tangent to the circle at C intersects AB produced in D. show that BC = BD.
Tangent at P to the circumcircle of triangle PQR is drawn. If the tangent is parallel to side, QR show that ΔPQR is isosceles.
In the given figure, O is the centre of the circle. Tangents at A and B meet at C. If ∠ACO = 30°, find:
- ∠BCO
- ∠AOB
- ∠APB
TA and TB are tangents to a circle with centre O from an external point T. OT intersects the circle at point P. Prove that AP bisects the angle TAB.
In the given figure, XY is the diameter of the circle and PQ is a tangent to the circle at Y.
If ∠AXB = 50° and ∠ABX = 70°, find ∠BAY and ∠APY.
In the following figure, PQ and PR are tangents to the circle, with centre O. If ∠ QPR = 60° , calculate:
∠ OQR
PT is a tangent to the circle at T. If ∠ ABC = 70° and ∠ ACB = 50° ; calculate : ∠ APT
The figure shows a circle of radius 9 cm with 0 as the centre. The diameter AB produced meets the tangent PQ at P. If PA = 24 cm, find the length of tangent PQ:
