<p>The circle \(x^2 + y^2 - 2x + 7y - 8 = 0\) cuts the \(x\)-axis at \(A\) and \(B\) and the \(y\)-axis at \(C\) and \(D\).</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Show that&nbsp;\(OA \times OB = OC \times OD\), where&nbsp;\(O\) is the origin.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Show that&nbsp;\(OA^2 + OB^2 + OC^2 + OD^2 = 4r^2\), where&nbsp;\(r\) is the radius of the circle.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Show that&nbsp;\(AD \times BC + AC \times BD = AB \times CD\).</span></div></li></ol>

The circle \(x^2 + y^2 - 2x + 7y - 8 = 0\) cuts the \(x\)-axis at \(A\) and \(B\) and the \(y\)-axis at \(C\) and \(D\).

Show that \(OA \times OB = OC \times OD\), where \(O\) is the origin.

Show that \(OA^2 + OB^2 + OC^2 + OD^2 = 4r^2\), where \(r\) is the radius of the circle.

Show that \(AD \times BC + AC \times BD = AB \times CD\).

Further Coordinate Geometry

Further Coordinate Geometry