Today our topic of discussion is Mathematics Circle Exercises 8.1.
Mathematics Circle Exercises 8.1
Exercise 8.1
- Prove that the straight line joining the middle points of two parallel chords of a circle passes through the centre and is perpendicular to the chords.
- Two chords AB and AC of a circle subtend equal angles with the radius passing through A. Prove that, AB = AC 3. A circle passes through the vertices of a right angled triangle. Show that, the centre of the circle is the middle point of the hypotenuse.
- A chord AB of one of the two concentric circles intersects the other circle at points C and D. Prove that, AC = BD
- If two equal chords of a circle intersect each other, show that two segments of one are equal to two segments of the other.
- Show that, the two equal chords drawn from two ends of the diameter on its opposite sides are parallel.
- Show that, of the two chords of a circle the bigger chord is nearer to the centre than the smaller.
- A chord PQ = xcm of a circle with the centre O and OR perp PQ .
1) What is the measurement of angle QOS ?
2) Prove that, the chord PS is the largest chord of the circle.
3) If OR = (x/2 – 2) measurement of z. cm, find out the
- Prove that if the straight line joining two points make equal angles at two different points on the same side of the straight line, then all these four points are concentric.
- Prove that, the middle points of equal chords of a circle are concyclic
- Show that, the two parallel chords of a circle drawn from two ends of a diameter on its opposite sides are equal.
- Prove that, if two chords of a circle bisect each other, their point of intersection is the centre of the circle.
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