Advertisements
Advertisements
प्रश्न
Prove that the line segment joining the midpoints of two parallel chords of a circle passes through its centre.
उत्तर
Given: AB and CO are two chords of a cirde with centre O.
AB II CD , M and N are midpoints of AB and CO respectively.
To prove : MN passes through centre O.
Construction : Join OM, ON, and through O, draw a straight line EF parallel to AB.
Proof : OM ⊥ AB
(line joining the midpoin t of a chord to the centre of a circle is perpendicular to it)
∠ AMO = 90°
∠ MOE = 90° [cointerior angle of ∠ AMO]
∠ NOE = 90° [corresponding angle of ∠ AMO]
∠ MOE + ∠ NOE = 180°
∠ MON is a straight line .
Hence, MN passes through centre O.
APPEARS IN
संबंधित प्रश्न
In the following figure, AD is a straight line. OP ⊥ AD and O is the centre of both the circles. If OA = 34 cm. OB = 20 cm and OP = 16cm; find the length of AB.
In the following figure; P and Q are the points of intersection of two circles with centres O and O’. If straight lines APB and CQD are parallel to O O'; prove that:
(i) O O' = `1/2AB` (ii) AB = CD
The length of common chord of two intersecting circles is 30 cm. If the diameters of these two circles be 50 cm and 34 cm, calculate the distance between their centres.
In the figure, AB is common chord of the two circles. If AC and AD are diameters; prove that D, B and C are in a straight line. O1 and O2 are the centers of two circles.
In the figure, chords AE and BC intersect each other at point D. If ∠CDE = 90°, AB = 5 cm, BD = 4 cm and CD = 9 cm; find DE.
In the figure, AB is the chord of a circle with centre O and DOC is a line segment such that BC = DO. If ∠C = 20°, find angle AOD.
In the given figure, QAP is the tangent at point A and PBD is a straight line.
If ∠ACB = 36° and ∠APB = 42°, find:
- ∠BAP
- ∠ABD
- ∠QAD
- ∠BCD
In the given figure, AB is the diameter. The tangent at C meets AB produced at Q.
If ∠CAB = 34°, Find : ∠CBA
Two circles are drawn with sides AB, AC of a triangle ABC as diameters. They intersect at a point D. Prove that D lies on BC.
In following figure . O is the centre of the circle. Find ∠ BAC.
