Advertisements
Advertisements
प्रश्न
In the given figure, M is the centre of the circle. Chords AB and CD are perpendicular to each other.
If ∠MAD = x and ∠BAC = y , Prove that : x = y
उत्तर
In the figure, M is the centre of the circle.
Chords AB and CD are perpendicular to each other at L.
∠MAD = x and ∠BAC = y
we have, ∠ABD =90° - y and ∠ABD = 90° - x [proved]
∴ 90° - x 90° - y
⇒ x = y
APPEARS IN
संबंधित प्रश्न
A chord of length 8 cm is drawn at a distance of 3 cm from the centre of a circle. Calculate the radius of the circle.
The radius of a circle is 17.0 cm and the length of perpendicular drawn from its centre to a chord is 8.0 cm. Calculate the length of the chord.
In a circle of radius 17 cm, two parallel chords of lengths 30 cm and 16 cm are drawn. Find the distance between the chords, if both the chords are
(i) on the opposite sides of the centre,
(ii) on the same side of the centre.
The figure given below, shows a circle with centre O in which diameter AB bisects the chord CD at point E. If CE = ED = 8 cm and EB = 4cm, find the radius of the circle.
In the following figure, the line ABCD is perpendicular to PQ; where P and Q are the centres of
the circles. Show that:
(i) AB = CD,
(ii) AC = BD.
In the given figure, AC is a diameter of a circle, whose centre is O. A circle is described on AO as diameter. AE, a chord of the larger circle, intersects the smaller circle at B. Prove that : AB = BE.
PQ and QR are two equal chords of a circle. A diameter of the circle is drawn through Q . Prove that the diameter bisects ∠ PQR.
In the given figure, M is the centre of the circle. Chords AB and CD are perpendicular to each other.
If ∠MAD = x and ∠BAC = y : express ∠ABD in terms of y.
The figure shows two concentric circles and AD is a chord of a larger circle.
Prove that: AB = CD.
AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24 cm. If the chords are on the opposite sides of the centre and the distance between them is 17 cm, find the radius of the circle.