In Figure, if /A O B=80^0a n d\ /A B C...

In Figure, if `/_A O B=80^0a n d\ /_A B C=30^0,` then find `/_C A O`

Text Solution

Verified by Experts

` arc AB` subtends `/_AOB` at the centre
`/_ACB` at the remaining part of the circle
`/_ACB=1/2/_AOB=1/2xx80^0=40^0`
In `/_\ OAB ,OA=AB`
`/_OAB=/_OBA`
`/_OAB+/_OBA+/_AOB=180^0`
`/_OAB+/_OBA+80^0=180^0`
`/_OAB+/_OAB=180^0-80^0`
`/_OAB=100^0/2=50^0`
Similarly in `/_\ABC, /_BAC+/_ACB+/_ABC=180^0`
`/_BAC+40^0+30^0=180^0`
`/_BAC=180^0-70^0=110^0`
`/_CAO=/_BAC-/_OAB=110^0-50^0=60^0`

Topper's Solved these Questions

AREA OF PARALLELOGRAMS AND TRIANGLES
RD SHARMA|Exercise All Questions|205 Videos
CONGRUENT TRIANGLE
RD SHARMA|Exercise All Questions|291 Videos

Similar Questions

Explore conceptually related problems

In Figure, if E C A B , /_E C D=70^0A N D /_B D O=20^0 , then /_O B D is: 20^0 (b) 50^0 (c) 60^0 (d) 70^0

A B C D is a cyclic quadrilateral in which: B C A D ,\ /_A D C=110^0\ a n d\ /_B A C=50^0dot Find /_D A C /_D B C=80^0\ a n d\ /_B A C=40^0dot Find /_B C D /_B C D=100^0a n d\ /_A B D=70^0 find /_A D B

In Figure, if A B||C D , /_A P Q=50^0A N D /_P R D=127^0, find x a n d y

The diagonals of a parallelogram A B C D intersect at O . If /_B O C=90^0\ a n d\ /_B D C=50^0, then /_O A B= 40^0 (b) 50^0 (c) 10^0 (d) 90^0

A B C D is a cyclic quadrilateral such that /_A D B=30^0a n d /_D C A=80^0, the /_D A B= 70^0 (b) 100^0 (c) 125^0 (d) 150^0

In Fig.104, A B C D ,\ /_O A B=150^0\ a n d\ /_O C D=120^0dot Then, /_A O C= (a) ( b ) (c) (d) (e) 80^(( f )0( g ))( h ) (i) (j) (b) ( k ) (l) (m) (n) 90^(( o )0( p ))( q ) (r) (s) (c) ( d ) (e) (f) (g) 70^(( h )0( i ))( j ) (k) (l) (d) ( m ) (n) (o) (p) 100^(( q )0( r ))( s ) (t) (u)

In a parallelogram A B C D , the diagonals bisect each other at Odot If /_A B C=30^0,\ /_B D C=10^0a n d\ /_C A B=70^0, Find: /_D A B ,\ /_A D C ,\ /_B C D ,\ /_A O D ,\ /_D O C ,\ /_B O C ,\ /_A O B ,\ /_A C D ,\ /_C A B ,\ /_A D B

In a DeltaA B C , if b=sqrt(3), c=1 a n d /_A=30^0, then find a

The side B C of A B C is produced to a point Ddot The bisector of /_A meets side B C in Ldot If /_A B C=30^0a n d /_A C D=115^0, then /_A L C= 85^0 (b) 72 1/2^0 (c) 145^0 (d) none of these

In Figure, P Q||R S , /_A E F=95^0, /_B H S=110^0 a n d /_A B C=x^0dot Then the value of x is (a)15^0 (b) 25^0 (c) 70^0 (d) 35^0

RD SHARMA-CIRCLE -All Questions

In Figure, two congruent circles with centers O\ a n d\ O ' intersec...
Text Solution
|
A B C D is a cyclic quadrilateral in which /B A D=75^0,\ /A B D=58^0...
Text Solution
|
In Figure, if /A O B=80^0a n d\ /A B C=30^0, then find /C A O
Text Solution
|
If O is the circumcentre of A B C , then find the value of /O B C...
Text Solution
|
If Figure, A O C is a diameter of the circle and are A X B=1/2 arc B...
Text Solution
|
In Figure, A is the centre of the circle. A B C D is a parallelogram...
Text Solution
|
In Figure, A B is a diameter of the circle such that /A=35^0a n d\ /...
Text Solution
|
In Figure, P\ a n d\ Q are centres of two circles intersecting at B\...
Text Solution
|
In Figure, A B C D is quadrilateral inscribed in a circle with centr...
Text Solution
|
If the length of a chord of a circle is 16 cm and is at a distance o...
Text Solution
|
The radius of a circle is 6 cm. The perpendicular distance from the ...
Text Solution
|
If O is the centre of a circle with radius r and AB is a chord of the ...
Text Solution
|
A B C D is a cyclic quadrilateral such that /A D B=30^0a n d\ /D C A...
Text Solution
|
A chord of length 14cm is at a distance of 6 cm from the center of the...
Text Solution
|
One chord of a circle is known to be 10 cm. The radius of this circl...
Text Solution
|
A B C is a triangle with B as right angle, A C=5\ c m\ a n d\ A B=...
Text Solution
|
If A B ,\ B C\ a n d\ C D are equal chords of a circle with O as cen...
Text Solution
|
Let C be the mid-point of an arc A B of a circle such that m\ hat...
Text Solution
|
In a circle, the major arc is 3 times the minor arc. The correspondi...
Text Solution
|
An equilateral triangle A B C is inscribed in a circle with centre...
Text Solution
|