Advertisements
Advertisements
प्रश्न
In the figure, O is the centre of a circle and diameter AB bisects the chord CD at a point E such that CE = ED = 8 cm and EB = 4 cm. The radius of the circle is
पर्याय
8 cm
4 cm
6 cm
10 cm
Advertisements
उत्तर
10 cm
Explanation;
Hint:
Let the radius OD be x.
OE = OB – BE
= x – 4 ...(OB radius of the circle)
In the ΔOED,
OD2 = OE2 + ED2
x2 = (x – 4)2 + 82
x2 = x2 + 16 – 8x + 64
8x = 80
x = `80/8`
= 10 cm
Radius of the circle = 10 cm.
APPEARS IN
संबंधित प्रश्न
In the given figure, tangents PQ and PR are drawn from an external point P to a circle with centre O, such that ∠RPQ = 30°. A chord RS is drawn parallel to the tangent PQ. Find ∠RQS.
Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?
O is the centre of a circle of radius 10 cm. P is any point in the circle such that OP = 6 cm. A is the point travelling along the circumference. x is the distance from A to P. what are the least and the greatest values of x in cm? what is the position of the points O, P and A at these values?
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.
ABC is a right triangle in which ∠B = 90°. If AB = 8 cm and BC = 6 cm, find the diameter of the circle inscribed in the triangle.
Twice the radius is ________________
Circles with centres A, B and C touch each other externally. If AB = 3 cm, BC = 3 cm, CA = 4 cm, then find the radii of each circle.
In the adjoining figure, seg DE is the chord of the circle with center C, seg CF ⊥ seg DE and DE = 16 cm, then find the length of DF?
If a number of circles pass through the endpoints P and Q of a line segment PQ, then their centres lie on the perpendicular bisector of PQ.
AB is a chord of a circle with centre O. AOC is diameter of circle, AT is a tangent at A.
Write answers of the following questions:
- Draw the figure using the given information.
- Find the measures of ∠CAT and ∠ABC with reasons.
- Whether ∠CAT and ∠ABC are congruent? Justify your answer.
