Advertisements
Advertisements
प्रश्न
In the given figure, O is the centre of the circle such that ∠AOC = 130°, then ∠ABC =
पर्याय
130°
115°
65°
165°
Advertisements
उत्तर
115°
We have the following information in the following figure. Take a point P on the circle in the given figure and join AP and CP.
Since, the angle subtended by a chord at the centre is twice that of subtended atany part of the circle.
So, `angleAPC = (angleAOC)/2 = 130/2 = 65°`
Since `squareAPBP` is a cyclic quadrilateral and we known that opposite angles are supplementary.
Therefore,
\[ \Rightarrow \angle ABC + 65° = 180° \]
\[ \Rightarrow \angle ABC = 180° - 65° \]
\[ \Rightarrow \angle ABC = 115°\]
APPEARS IN
संबंधित प्रश्न
Two chords AB and CD of lengths 5 cm 11cm respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between AB and CD is 6 cm, find the radius of the circle.
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 figure, `square`ABCD is a cyclic quadrilateral. Seg AB is a diameter. If ∠ ADC = 120˚, complete the following activity to find measure of ∠ BAC.
`square` ABCD is a cyclic quadrilateral.
∴ ∠ ADC + ∠ ABC = 180°
∴ 120˚ + ∠ ABC = 180°
∴ ∠ ABC = ______
But ∠ ACB = ______ .......(angle in semicircle)
In Δ ABC,
∠ BAC + ∠ ACB + ∠ ABC = 180°
∴ ∠BAC + ______ = 180°
∴ ∠ BAC = ______
In the given figure, ABCD is a cyclic quadrilateral. Find the value of x.
Prove that the centre of the circle circumscribing the cyclic rectangle ABCD is the point of intersection of its diagonals.
ABCD is a cyclic quadrilateral. M (arc ABC) = 230°. Find ∠ABC, ∠CDA, and ∠CBE.
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.
If non-parallel sides of a trapezium are equal, prove that it is cyclic.
ABCD is a parallelogram. A circle through A, B is so drawn that it intersects AD at P and BC at Q. Prove that P, Q, C and D are concyclic.
