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
A chord PQ of a circle of radius 10 cm substends an angle of 60° at the centre of circle. Find the area of major and minor segments of the circle.
Fill in the blank:
A point whose distance from the centre of a circle is greater than its radius lies in ..................... of the circle.
PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the lengths of TP and TQ.
In Fig. 5, the chord AB of the larger of the two concentric circles, with centre O, touches the smaller circle at C. Prove that AC = CB.
In the given figure, if ABC is an equilateral triangle. Find ∠BDC and ∠BEC.
The radius of a circle is 6 cm. The perpendicular distance from the centre of the circle to the chord which is 8 cm in length, is
In the above figure, seg AB is a diameter of a circle with centre P. C is any point on the circle. seg CE ⊥ seg AB. Prove that CE is the geometric mean of AE and EB. Write the proof with the help of the following steps:
a. Draw ray CE. It intersects the circle at D.
b. Show that CE = ED.
c. Write the result using the theorem of the intersection of chords inside a circle. d. Using CE = ED, complete the proof.
Find the missing values in the following table for the circles with radius (r), diameter (d) and Circumference (C).
| radius (r) | diameter (d) | Circumference (C) |
| 15 cm |
Find the missing values in the following table for the circles with radius (r), diameter (d) and Circumference (C).
| radius (r) | diameter (d) | Circumference (C) |
| 24 m |
Draw two acute angles and one obtuse angle without using a protractor. Estimate the measures of the angles. Measure them with the help of a protractor and see how much accurate is your estimate.
