Advertisements
Advertisements
Questions
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
Solution
(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°.
RELATED QUESTIONS
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.
Two circles intersect at P and Q. Through P diameters PA and PB of the two circles are drawn. Show that the points A, Q and B are collinear.
In the figure, given alongside, AB || CD and O is the centre of the circle. If ∠ADC = 25°; find the angle AEB. Give reasons in support of your answer.
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
Prove that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base.
In the given figure, AB is a diameter of the circle with centre O. DO is parallel to CB and ∠DCB = 120°.
Calculate : ∠DBA
Also, show that the ΔAOD is an equilateral triangle.
In the given figure, O is the centre of the circle and ∠PBA = 45°. Calculate the value of ∠PQB.
In Fig, Chord ED is parallel to the diameter AC of the circle. Given ∠CBE = 65°, Calculate ∠ DEC.
In the figure, ∠DBC = 58°. BD is diameter of the circle.
Calculate:
- ∠BDC
- ∠BEC
- ∠BAC
