Advertisements
Advertisements
प्रश्न
ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 140º, then ∠BAC is equal to ______.
पर्याय
80º
50º
40º
30º
Advertisements
उत्तर
ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 140º, then ∠BAC is equal to 50º.
Explanation:
Given, ABCD is a cyclic quadrilateral and ∠ADC = 140°.
We know that, sum of the opposite angles in a cyclic quadrilateral is 180°.
∠ADC + ∠ABC = 180°
⇒ 140° + ∠ABC = 180°
⇒ ∠ABC = 180° – 140°
∴ ∠ABC = 40°
Since, ∠ACB is an angle in a semi-circle.
∴ ∠ACB = 90°
In ΔABC, ∠BAC + ∠ACB + ∠ABC = 180° ...[By angle sum property of a triangle]
⇒ ∠BAC + 90° + 40° = 180°
⇒ ∠BAC = 180° – 130° = 50°
APPEARS IN
संबंधित प्रश्न
ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC = 70°, ∠BAC is 30°, find ∠BCD. Further, if AB = BC, find ∠ECD.
Prove that a cyclic parallelogram is a rectangle.
ABCD is a parallelogram. The circle through A, B and C intersect CD (produced if necessary) at E. Prove that AE = AD.
In the given figure, ∠BAD = 78°, ∠DCF = x° and ∠DEF = y°. Find the values of x and y.
In the given figure, ABCD is a cyclic quadrilateral. Find the value of x.
ABCD is a cyclic quadrilateral in BC || AD, ∠ADC = 110° and ∠BAC = 50°. Find ∠DAC.
ABCD is a cyclic quadrilateral in ∠BCD = 100° and ∠ABD = 70° find ∠ADB.
In the given figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠DBC = 55° and ∠BAC = 45°, find ∠BCD.
Prove that the centre of the circle circumscribing the cyclic rectangle ABCD is the point of intersection of its diagonals.
If a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are also equal.
