Advertisements
Advertisements
प्रश्न
In the following figure, ∠ADC = 130° and chord BC = chord BE. Find ∠CBE.
In the given figure, AB is a diameter of the circle with centre O. If ∠ADC = 130° and chord BC = chord BE, find ∠CBE.
Advertisements
उत्तर
Let us consider the points A, B, C, and D, which form a cyclic quadrilateral.
∴ ∠ADC + ∠OBC = 180° ... [The sum of opposite angles of a cyclic quadrilateral is 180°.]
⇒ 130° + ∠ABC = 180°
⇒ ∠ABC = 180° – 130° = 50°
In ΔBOC and ΔBOE,
BC = BE ...[Given]
OC = OE ... [Radii of a same circle]
And OB = OB ...[Common]
∴ ΔBOC ≅ ΔBOE ...[By SSS congruency]
⇒ ∠OBC = ∠OBE ...[By C.P.C.T]
Now, ∠CBE = ∠OBC + ∠OBE
= 50° + 50°
= 100°
APPEARS IN
संबंधित प्रश्न
In Figure 1, common tangents AB and CD to the two circles with centres 01and 02 intersect at E. Prove that AB = CD.
In fig. XP and XQ are tangents from X to the circle with centre O. R is a point on the circle. Prove that, XA + AR = XB + BR.
If AB, AC, PQ are tangents in Fig. and AB = 5 cm find the perimeter of ΔAPQ.
In the given figure, if ∠BAC = 60° and ∠BCA = 20°, find ∠ADC.
Equal circles with centres O and O' touch each other at X. OO' produced to meet a circle with centre O', at A. AC is a tangent to the circle whose centre is O. O'D is perpendicular to AC. Find the value of\[\frac{DO'}{CO}\]
In Fig., chords AB and CD of the circle intersect at O. AO = 5 cm, BO = 3 cm and CO = 2.5 cm. Determine the length of DO.
If the radius of a circle is 5 cm, what will its diameter be?
Find the diameter of the circle
Radius = 6 cm
Circles with centres A, B and C touch each other externally. If AB = 3 cm, BC = 3 cm, CA = 4 cm, then find the radii of each circle.
In the following figure, O is the centre of the circle. Shade sectors OAC and OPB.
