Advertisements
Advertisements
Question
Prove that a diameter of a circle which bisects a chord of the circle also bisects the angle subtended by the chord at the centre of the circle.
Advertisements
Solution
Given: PQ is a diameter of circle which Bisects
Chord AB at C
To prove: PQ bisects ∠AOB
Proof:
In ΔAOC and ΔBOC
OA=OB
OC=OC
AC=BC
Then Δ AOC ≅ BOC
∴∠AOC = ∠BOC
Hence PQ bisects ∠AOB
APPEARS IN
RELATED QUESTIONS
In the given figure, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130° and ∠ECD = 20°. Find ∠BAC.
Fill in the blank:
Segment of a circle is the region between an arc and .................. of the circle.
Prove that the line joining the mid-point of a chord to the centre of the circle passes through the mid-point of the corresponding minor arc.
If O is the centre of the circle, find the value of x in the following figure
If O is the centre of the circle, find the value of x in the following figure
If O is the centre of the circle, find the value of x in the following figure
In the given figure, O and O' are centres of two circles intersecting at B and C. ACD is a straight line, find x.
In the given figure, O is the centre of a circle and PQ is a diameter. If ∠ROS = 40°, find ∠RTS.
In the given figure, AB is a diameter of the circle such that ∠A = 35° and ∠Q = 25°, find ∠PBR.
A chord of a circle is equal to its radius. Find the angle subtended by this chord at a point in major segment.
