Advertisements
Advertisements
Question
In the Figure, PT is a tangent to a circle. If m(∠BTA) = 45° and m(∠PTB) = 70°. Find m(∠ABT).
Solution
∠ ATP = ∠ PTB - ∠ BTA
= 70° - 45° = 25°
∴ ∠ ABT = ∠ ATP ...(Angles are in alternate segments)
⇒ ∠ ABT = 25°.
APPEARS IN
RELATED QUESTIONS
From a point P outside a circle, with centre O, tangents PA and PB are drawn. Prove that:
∠AOP = ∠BOP
Tangents AP and AQ are drawn to a circle, with centre O, from an exterior point A. Prove that : ∠PAQ = 2∠OPQ
In a triangle ABC, the incircle (centre O) touches BC, CA and AB at points P, Q and R respectively. Calculate:
i)`∠`QPR .
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°.
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
A circle touches the sides of a quadrilateral ABCD at P, Q, R, S respectively. Show that the angles subtended at the centre by a pair of opposite sides are supplementary.
In the given figure, AB is the diameter. The tangent at C meets AB produced at Q. If ∠CAB = 34°, find:
- ∠CBA
- ∠CQB
In the joining figure shown XAY is a tangent. If ∠ BDA = 44°, ∠ BXA = 36°.
Calculate: (i) ∠ BAX, (ii) ∠ DAY, (iii) ∠ DAB, (iv) ∠ BCD.
In the adjoining diagram TA and TB are tangents, O is the centre. If ∠ PAT = 35° and ∠ PBT = 40°.
Calculate:
(i) ∠ AQP, (ii) ∠ BQP
(iii) ∠ AQB, (iv) ∠ APB
(v) ∠ AOB, (vi) ∠ ATB
