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
In the given figure, ∠PQR = 100°, where P, Q and R are points on a circle with centre O. Find ∠OPR.
If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.
If the non-parallel sides of a trapezium are equal, prove that it is cyclic.
If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.
ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD = ∠CBD.
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 a cyclic quadrilateral ABCD, if ∠A − ∠C = 60°, prove that the smaller of two is 60°
If the two sides of a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are equal.
In the figure, ▢ABCD is a cyclic quadrilateral. If m(arc ABC) = 230°, then find ∠ABC, ∠CDA, ∠CBE.
If non-parallel sides of a trapezium are equal, prove that it is cyclic.
