Advertisements
Advertisements
प्रश्न
The following figure shows a circle with PR as its diameter. If PQ = 7 cm and QR = 3RS = 6 cm, find the perimeter of the cyclic quadrilateral PQRS.
Advertisements
उत्तर
In the figure, PQRS is a cyclic quadrilateral in which PR is a diameter
PQ = 7 cm
QR = 3RS = 6 cm
3RS = 6 cm
RS = 2 cm
Now in ∆PQR,
∠Q = 90° ...[Angles in a semi-circle]
∴ PR2 = PQ2 + QR2 ...[Pythagoras theorem]
= 72 + 62
= 49 + 36
= 85
Again in right ΔPSQ,
PR2 = PS2 + RS2
`=>` 85 = PS2 + 22
`=>` PS2 = 85 – 4 = 81 = (9)2
∴ PS = 9 cm
Now, perimeter of quad PQRS
= PQ + QR + RS + SP
= (7 + 9 + 2 + 6) cm
= 24
APPEARS IN
संबंधित प्रश्न
In the given figure, ∠BAD = 65°, ∠ABD = 70°, ∠BDC = 45°
1) Prove that AC is a diameter of the circle.
2) Find ∠ACB
ABC is a right angles triangle with AB = 12 cm and AC = 13 cm. A circle, with centre O, has been inscribed inside the triangle.
Calculate the value of x, the radius of the inscribed circle.
Prove that the parallelogram, inscribed in a circle, is a rectangle.
Two circles intersect at P and Q. Through P diameters PA and PB of the two circles are drawn. Show that the points A, Q and B are collinear.
In the given figure, AB is a diameter of the circle with centre O. DO is parallel to CB and ∠DCB = 120°.
Calculate:
- ∠DAB,
- ∠DBA,
- ∠DBC,
- ∠ADC.
Also, show that the ΔAOD is an equilateral triangle.
In the given figure, RS is a diameter of the circle. NM is parallel to RS and ∠MRS = 29°. Calculate : ∠NRM
In the given figure, AB is a diameter of the circle with centre O. DO is parallel to CB and ∠DCB = 120°.
Calculate: ∠ADC
Also, show that the ΔAOD is an equilateral triangle.
In the following figure, AD is the diameter of the circle with centre O. chords AB, BC and CD are equal. If ∠DEF = 110°, Calculate: ∠FAB.
In Fig, Chord ED is parallel to the diameter AC of the circle. Given ∠CBE = 65°, Calculate ∠ DEC.
In the given figure, AC is the diameter of the circle with center O.
CD is parallel to BE.
∠AOB = 80° and ∠ACE = 20°
Calculate:
- ∠BEC
- ∠BCD
- ∠CED
