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The given figure shows two congruent circles with centre O and O’ intersecting at A and B. If ∠AO′B = 50o, then the measure of ∠APB is
- a)45o
- b)25o
- c)40o
- d)50o
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The given figure shows two congruent circles with centre O and O&rsquo...
Given both circles are congruent
so their radius are equal
so,OA = OB = O'B = O'A
TO Prove ∆OBA Congruent to ∆O'BA
proof
OA = O'A (Given above)
OB = O'B (Given above)
AB = AB (Common side)
so ∆OBA Congruent to ∆O'BA
angle AOB = angle AO'B (By CPCT)
AOB = 50 Degree
i) OA = OB
so angle OAB = Angle OBA
(opposite angles of equal sides are equal)
ii) angle OAB + Angle OBA + angle AOB = 180
2 OAB + AOB = 180
2 OAB = 180 - 50
2 OAB = 130
OAB = 130 ÷ 2
OAB = 65
SO OBA = 65
Take triangle PAB
Angle PBA = 65
Angle PAB = 90
(triangle with hypotenuse as diameter of circle , it's opposite angle is always 90 )
Angle P = 180 - PBA - PAB
P = 180 - 65 - 90
P = 25
hence 'b' is correct answer
so their radius are equal
so,OA = OB = O'B = O'A
TO Prove ∆OBA Congruent to ∆O'BA
proof
OA = O'A (Given above)
OB = O'B (Given above)
AB = AB (Common side)
so ∆OBA Congruent to ∆O'BA
angle AOB = angle AO'B (By CPCT)
AOB = 50 Degree
i) OA = OB
so angle OAB = Angle OBA
(opposite angles of equal sides are equal)
ii) angle OAB + Angle OBA + angle AOB = 180
2 OAB + AOB = 180
2 OAB = 180 - 50
2 OAB = 130
OAB = 130 ÷ 2
OAB = 65
SO OBA = 65
Take triangle PAB
Angle PBA = 65
Angle PAB = 90
(triangle with hypotenuse as diameter of circle , it's opposite angle is always 90 )
Angle P = 180 - PBA - PAB
P = 180 - 65 - 90
P = 25
hence 'b' is correct answer
Community Answer
The given figure shows two congruent circles with centre O and O&rsquo...
AOB= 50
PB is line .
POA +AOB=180 ( linear pair)
POA+50=180
POA=130
∆POA
OP=OA(radius of the circle)
so, angle P = angle A (because triangle POA is Isoscale)
A+O +P =180
P+O+P=180
2P+130=180
2P=50
P= 20
PB is line .
POA +AOB=180 ( linear pair)
POA+50=180
POA=130
∆POA
OP=OA(radius of the circle)
so, angle P = angle A (because triangle POA is Isoscale)
A+O +P =180
P+O+P=180
2P+130=180
2P=50
P= 20
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The given figure shows two congruent circles with centre O and O’ intersecting at A and B. If∠AO′B = 50o,then the measure of∠APB isa)45ob)25oc)40od)50oCorrect answer is option 'B'. Can you explain this answer?
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