Advertisements
Advertisements
Question
In the given figure, AB and CD are diameters of a circle with centre O. If ∠OBD = 50°, find ∠AOC.
Advertisements
Solution
It is given that, AB and CD are diameter with center O and `angleOBD = 50°`
We have to find `angle AOC`
Construction: Join the point A and D to form line AD
Clearly arc AD subtends`angle ABD = 50°` at B and `angleAOD` at the centre.
Therefore,
Since CD is a straight line then
APPEARS IN
RELATED QUESTIONS
Fill in the blanks:
A point, whose distance from the centre of a circle is greater than its radius lies in __________ of the circle. (exterior/ interior)
If from any point on the common chord of two intersecting circles, tangents be drawn to circles, prove that they are equal.
Two tangent segments PA and PB are drawn to a circle with center O such that ∠APB = 120°. Prove that OP = 2AP
If ΔABC is isosceles with AB = AC and C (0, 2) is the in circle of the ΔABC touching BC at L, prove that L, bisects BC.
In the given figure, AB is a side of a regular six-sided polygon and AC is a side of a regular eight-sided polygon inscribed in the circle with centre O. Calculate the sizes of:
- ∠AOB,
- ∠ACB,
- ∠ABC.
In the given figure, O is the centre of the two concentric circles of radii 4 cm and 6cm respectively. AP and PB are tangents to the outer and inner circle respectively. If PA = 10cm, find the length of PB up to one place of the decimal.
The greatest chord of a circle is called its
AB and CD are common tangents to two circles of equal radii. Prove that AB = CD.
Equal circles with centres O and O' touch each other at X. OO' produced to meet a circle with centre O', at A. AC is a tangent to the circle whose centre is O. O'D is perpendicular to AC. Find the value of\[\frac{DO'}{CO}\]
The diameter of the circle is 52 cm and the length of one of its chord is 20 cm. Find the distance of the chord from the centre
