Advertisements
Advertisements
प्रश्न
ABCD is a cyclic quadrilateral in which AB is parallel to DC and AB is a diameter of the circle. Given ∠BED = 65°, calculate:
- ∠DAB,
- ∠BDC.
ABCD is a cyclic quadrilateral and DC || AB. If AB is the diameter of the circle and BED = 65°, find:
- ∠DAB
- ∠BDC
Advertisements
उत्तर
(i) Find ∠DAB
Angles BED and DAB are angles subtended by the same chord DB in the same circle.
∴ ∠DAB = ∠BED = 65°
(ii) Find ∠BDC
Since AB is a diameter, angle ADB is an angle in a semicircle:
∠ADB = 90°.
In triangle ABD:
∠ABD = 180° − (∠ADB + ∠DAB)
∠ABD = 180° − (90° + 65°)
∠ABD = 25°.
AB ∥ DC,
∠ABD and ∠BDC are corresponding angles.
∴∠BDC = ∠ABD = 25°.
APPEARS IN
संबंधित प्रश्न
Calculate the area of the shaded region, if the diameter of the semicircle is equal to 14 cm. Take `pi = 22/7`
Prove that the parallelogram, inscribed in a circle, is a rectangle.
In the given figure, AB is a diameter of the circle. Chord ED is parallel to AB and ∠EAB = 63°.
Calculate:
- ∠EBA,
- ∠BCD.
In the following figure, AD is the diameter of the circle with centre O. Chords AB, BC and CD are equal. If ∠DEF = 110°, calculate: ∠AEF
In the given figure, AB is the diameter of a circle with centre O.
If chord AC = chord AD, prove that:
- arc BC = arc DB
- AB is bisector of ∠CAD.
Further, if the length of arc AC is twice the length of arc BC, find:
- ∠BAC
- ∠ABC
In the figure, given below, AB and CD are two parallel chords and O is the centre. If the radius of the circle is 15 cm, find the distance MN between the two chords of lengths 24 cm and 18 cm respectively.
Using ruler and a compass only construct a semi-circle with diameter BC = 7cm. Locate a point A on the circumference of the semicircle such that A is equidistant from B and C. Complete the cyclic quadrilateral ABCD, such that D is equidistant from AB and BC. Measure ∠ADC and write it down.
In the given figure, AB is a diameter of the circle with centre O. DO is parallel to CB and ∠DCB = 120°.
Calculate : ∠DBC
Also, show that the ΔAOD is an equilateral triangle.
In the following figure, AD is the diameter of the circle with centre O. chords AB, BC and CD are equal. If ∠DEF = 110°, Calculate: ∠FAB.
In the figure, ∠DBC = 58°. BD is diameter of the circle.
Calculate:
- ∠BDC
- ∠BEC
- ∠BAC
