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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 March 2013, 8:36 PM
Answered by Expert
Answer:
 
 
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 Expert 14th March 2013, 10:45 PM
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