Advertisements
Advertisements
प्रश्न
In the following figure, AOB is a diameter of the circle and C, D, E are any three points on the semi-circle. Find the value of ∠ACD + ∠BED.
Advertisements
उत्तर
Since, A, C, D and E are four point on a circle, then ACDE is a cyclic quadrilateral.
∠ACD + ∠AED = 180° ...(i) [Sum of opposite angles in a cyclic quadrilateral is 180°]
Now, ∠AEB = 90° ...(ii)
We know that, diameter subtends a right angle to the circle.
On adding equations (i) and (ii), we get
(∠ACD + ∠AED) + ∠AEB = 180° + 90° = 270°
⇒ ∠ACD + ∠BED = 270°
APPEARS IN
संबंधित प्रश्न
Prove that ‘Opposite angles of a cyclic quadrilateral are supplementary’.
ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD = ∠CBD.
Prove that a cyclic parallelogram is a rectangle.
The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the centre, what is the distance of the other chord from the centre?
In the figure m(arc LN) = 110°,
m(arc PQ) = 50° then complete the following activity to find ∠LMN.
∠ LMN = `1/2` [m(arc LN) - _______]
∴ ∠ LMN = `1/2` [_________ - 50°]
∴ ∠ LMN = `1/2` × _________
∴ ∠ LMN = __________
In the given figure, ABCD is a cyclic quadrilateral. Find the value of x.
ABCD is a cyclic quadrilateral in which BA and CD when produced meet in E and EA = ED. Prove that EB = EC.
PQRS is a cyclic quadrilateral such that PR is a diameter of the circle. If ∠QPR = 67° and ∠SPR = 72°, then ∠QRS =
If a line is drawn parallel to the base of an isosceles triangle to intersect its equal sides, prove that the quadrilateral so formed is cyclic.
If a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are also equal.
