Advertisements
Advertisements
Question
In the following figure, O is the centre of the circle. Find the values of a, b, c and d.
Solution
∠APB = 90° (Angle in a semicircle)
∴ ∠BAP = 90° – 45° = 45°
Now, d = ∠BCP = ∠BAP = 45°
(Angle subtended by the same chord on the circle are equal)
APPEARS IN
RELATED QUESTIONS
In the figure given below AB and CD are two parallel chords and O is the centre. If the radius of the circle is 15 cm, find the distance MN between the two chords of length 24 cm and 18 cm respectively.
AB and CD are two equal chords of a circle with centre O which intersect each other at right
angle at point P. If OM⊥ AB and ON ⊥ CD; show that OMPN is a square.
In the following figure, O is the centre of the circle. Find the values of a, b, c and d.
Calculate:
- ∠CDB,
- ∠ABC,
- ∠ACB.
In the given figure, I is the incentre of ΔABC. BI when produced meets the circumcircle of ΔABC at D. ∠BAC = 55° and ∠ACB = 65°; calculate:
- ∠DCA,
- ∠DAC,
- ∠DCI,
- ∠AIC.
In the figure, chords AE and BC intersect each other at point D. If AD = BD, show that AE = BC.
The length of the common chord of two intersecting circles is 30 cm. If the diameters of these two circles are 50 cm and 34 cm, calculate the distance between their centers.
Given two equal chords AB and CD of a circle with center O, intersecting each other at point P.
Prove that:
(i) AP = CP
(ii) BP = DP
If a diameter of a circle bisects each of the two chords of a circle, prove that the chords are parallel.
Two chords AB, CD of lengths 16 cm and 30 cm, are parallel. If the distance between AB and CD is 23 cm. Find the radius of the circle.
