Advertisements
Advertisements
Question
PT is a tangent to the circle at T. If ∠ ABC = 70° and ∠ ACB = 50° ; calculate : ∠ APT
Solution
Join AT and BT.
∠ BTX = ∠ TCB = 30° (Angles in the same segment)
∴ ∠ PTB = 180° - 30° = 150°
Now in Δ PTB ,
∠APT + ∠ PTB + ∠ ABT = 180°
⇒ ∠APT + 150° + 20° = 180°
⇒ ∠APT = 180° - 170° = 10°
APPEARS IN
RELATED QUESTIONS
In the given figure, O is the center of the circle and AB is a tangent at B. If AB = 15 cm and AC = 7.5 cm, calculate the radius of the circle.
If the sides of a quadrilateral ABCD touch a circle, prove that : AB + CD = BC + AD.
In a triangle ABC, the incircle (centre O) touches BC, CA and AB at points P, Q and R respectively. Calculate:
i)`∠`QPR .
In the given figure, PT touches the circle with centre O at point R. Diameter SQ is produced to meet the tangent TR at P. Given ∠SPR = x° and ∠QRP = y°;
Prove that:
- ∠ORS = y°
- write an expression connecting x and y.
PT is a tangent to the circle at T. If ∠ABC = 70° and ∠ACB = 50°; calculate:
- ∠CBT
- ∠BAT
- ∠APT
In the given figure, O is the centre of the circumcircle ABC. Tangents at A and C intersect at P. Given angle AOB = 140° and angle APC = 80°; find the angle BAC.
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 figure , ABC is an isosceles triangle inscribed in a circle with centre O such that AB = AC = 13 cm and BC = 10 cm .Find the radius of the circle.
In the given figure, PT touches a circle with centre O at R. Diameter SQ when produced to meet the tangent PT at P. If ∠SPR = x° and ∠QRP = y°; Show that x° + 2y° = 90°
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
