Mathematics
Two equal chords AB and CD of a circle with center O, intersect each other at point P inside the circle. Prove that :
(i) AP = CP
(ii) BP = DP
Related Questions
A straight line is drawn cutting two equal circles and passing through the mid-point M of the line joining their centers O and O'.
Prove that the chords AB and CD, which are intercepted by the two circles, are equal.
M and N are the mid-points of two equal chords AB and CD respectively of a circle with center O. Prove that :
(i) ∠BMN = ∠DNM
(ii) ∠AMN = ∠CNM.
In the following figure, OABC is a square. A circle is drawn with O as center which meets OC at P and OA at Q. Prove that :
(i) △ OPA ≅ △ OQC
(ii) △ BPC ≅ △ BQA
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 centers.