Home
Class 10
MATHS
In figure, AB is a chord of the circle a...

In figure, AB is a chord of the circle and AOC is the diameter such that `angleACB=50^(@)`. If AT is the tangent to the circle at the point A, then `angleBAT` is equal to : (a) `45^(@)` , (b) `60^(@)` , (c) `50^(@)` , (d) `55^(@)`

Text Solution

Verified by Experts

( c )
We know that the angle in a semicircle is `90^(@)`.
`because` AOC is a diameter.
`:." "angleABC=90^(@)`
In `triangleABC`
`angleBAC+angleABC+angleACB=180^(@)`
`implies" "angleBAC+90^(@)+50^(@)=180^(@)" "implies" "angleBAC=180^(@)-140^(@)=40^(@)`
Now AT is the tangent.
`:." "angleOAT=90^(@)`
`implies" "angleOAB-angleBAT=90^(@)`
`implies" "angleBAT=90^(@)-angleBAC=90^(@)-40^(@)=50^(@)`
Promotional Banner

Topper's Solved these Questions

  • CIRCLES

    NAGEEN PRAKASHAN|Exercise Exercise|25 Videos

  • CIRCLES

    NAGEEN PRAKASHAN|Exercise Revision Exercise Very Short Answer Question|7 Videos

  • CIRCLES

    NAGEEN PRAKASHAN|Exercise Revision Exercise Long Answer Questions|3 Videos

  • ARITHMETIC PROGRESSION

    NAGEEN PRAKASHAN|Exercise Revision Exercise Long Answer Question|5 Videos

  • CO-ORDINATE GEOMETRY

    NAGEEN PRAKASHAN|Exercise Revision Exercise Short Answer Questions|9 Videos

Similar Questions

Explore conceptually related problems

In figure, AB is a chord of the circle and AOC is its diameter such that angleACB=50^(@) . If AT is the tangent to the circle at the point A, then angleBAT is equal to

In the given figure A,B is a chord of the circle and AOC is its diameter ,such that angleACB=50^(@) .If AT is the tangent to the circle at the point A, then angleBAT is equal to :

AB is a diameter of a circle and AC is its chord such that angleBAC=30^(@) . If the tengent at C intersects AB extended at D, then BC=BD.

In fig AB is chord of a circle with centre O and AP is the tangent at A such that angleBAP = 75^@ find angleACB

In the figure, AB is the diameter of the circle. If angle AOC = 135^(@) then find the angle CDB .

In Figure-2 PQ is tangent to the circle with centre at O , at the point B. If angle AOB = 100^@ , then angle ABP is equal to (A) 50^@ (B) 40^@ (C) 60^@ (D) 80^@

In the above figure , O is the centre of the circle, AB and CD are diameters. /_ COB =50^(@)=50^(@) . If E is the midpoint of AF, then find /_ ADF