Advertisements
Advertisements
प्रश्न
In the figure alongside PR is a diameter of the circle, PQ = 7 cm; QR = 6 cm and RS = 2 cm. Calculate the perimeter of the cyclic quadrilateral PQRS.
उत्तर
PR is the diameter of the circle.
then ∠ PQR = 90° .....(Angle in semicircle)
In Δ PQR,
PR = `sqrt((7)^2 + (6)^2)`
PR = `sqrt(49 + 36)`
PR = `sqrt(85)`
Similarly,
∠ PSR = 90°
In ΔPSR,
PS = `sqrt("PR"^2 - "SR"^2)`
PS = `sqrt(85 - 4)`
PS = `sqrt(81)`
PS = 9 cm
Perimeter of cyclic quadrilateral PQRS = PQ + QR + RS + PS
Perimeter of cyclic quadrilateral PQRS = 7 cm + 6 cm + 2 cm + 9 cm = 24 cm
Perimeter of cyclic quadrilateral PQRS = 24 cm.
APPEARS IN
संबंधित प्रश्न
PQRS is a cyclic quadrilateral. Given ∠QPS = 73°, ∠PQS = 55° and ∠PSR = 82°, calculate:
1) ∠QRS
2) ∠RQS
3) ∠PRQ
In the figure, given below, find:
- ∠BCD,
- ∠ADC,
- ∠ABC.
Show steps of your working.
ABCD is a cyclic quadrilateral in which BC is parallel to AD, angle ADC = 110° and angle BAC = 50°. Find angle DAC and angle DCA.
D and E are points on equal sides AB and AC of an isosceles triangle ABC such that AD = AE. Prove that the points B, C, E and D are concyclic.
The given figure shows a semi-circle with centre O and diameter PQ. If PA = AB and ∠BCQ =140°; find measures of angles PAB and AQB. Also, show that AO is parallel to BQ.
In the given figure, PAT is tangent to the circle with centre O at point A on its circumference and is parallel to chord BC. If CDQ is a line segment, show that:
- ∠BAP = ∠ADQ
- ∠AOB = 2∠ADQ
- ∠ADQ = ∠ADB
ABCD is a cyclic quadrilateral of a circle with centre O such that AB is a diameter of this circle and the length of the chord CD is equal to the radius of the circle. If AD and BC produced meet at P, show that APB = 60°.
In following figure , O is the centre of the circle. If ∠ APB = 50° then find ∠ AOB and ∠ OAB.
ABCD is a parallelogram. A circle through vertices A and B meets side BC at point P and side AD at point Q. Show that quadrilateral PCDQ is cyclic.
If O is the centre of the circle, find the value of x in each of the following figures
