Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
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.
Given an arc of a circle, show how to complete the circle.
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, two circles intersect at A and B. The centre of the smaller circle is Oand it lies on the circumference of the larger circle. If ∠APB = 70°, find ∠ACB.
If ABC is an arc of a circle and ∠ABC = 135°, then the ratio of arc \[\stackrel\frown{ABC}\] to the circumference is ______.
The chord of a circle is equal to its radius. The angle subtended by this chord at the minor arc of the circle is
If arcs AXB and CYD of a circle are congruent, find the ratio of AB and CD.
A chord of a circle is equal to its radius. Find the angle subtended by this chord at a point in major segment.
In the following figure, ∠ACB = 40º. Find ∠OAB.
