Q.1. If two equal chords intersect within the circle , prove that the line joining the point of intersection to the centre makes equal angles with the chord ?? Q.2. A circular park of radius 25 cm is situated in a colony. three giirls ankita , anvita & goomal are siting on its boundary at equal distances. All the three girls having toy phone to talk with each other connected with string . Find the distance of the string between ankita & anvita ?? Q.3. Prove that the square formed by the internal angle bisectors of any quadrilateral is cyclic ?? Q.4.adjacent angles of a parallelogram are in the ratio 2:3 find the angles of the parallelogram ?? Q.5. adjacent angles of the parallelogram are (3x-40)degreesand (2x+20)degrees, find all the angles of the parallelogram ???
Asked by Kunwar Digvijay Singh Tanwar | 14th Mar, 2013, 08:36: PM
Answer : Given :If two equal chords intersect within the circle ,
To prove that the line joining the point of intersection to the centre makes equal angles with the chord
Let PQ and RS are two equal chords of a given circle and they are intersecting each other at point T.
Draw perpendiculars OV and OU on these chords.
In traingle OVT and triangle OUT,
OV = OU (Equal chords of a circle are equidistant from the centre)
angle OVT = angle OUT (Each 90 degree)
OT = OT (Common)
therefore ,triangle OVT is congruent to triangle OUT (RHS congruence rule)
therefore , angle OTV = angle OTU (By CPCT)
Therefore, it is proved that the line joining the point of intersection to the centre makes equal angles with the chords.
Answered by | 14th Mar, 2013, 10:45: PM
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