7746 /www/nrich/html/content/id/7746/ 1 0000-00-00T00:00:00 <mdoxml version="1.0"> <p>AB is a diameter. C is a point on the circle.</p> <p>Prove that $\angle ACB = 90^\circ$</p> <p><mdo:image src="ws1.png"></mdo:image></p> <p>A, B, C and D are points on the circle that form a quadrilateral.</p> <p>Prove that</p> <p> $\angle ABC + \angle ADC = \angle BAD + \angle BCD = 180^\circ$</p> <p><mdo:image src="ws2.png"></mdo:image></p> <p>A, B, C and D are points on the circle that form a quadrilateral.</p> <p>Prove that</p> <p> $\angle ABC + \angle ADC = \angle BAD + \angle BCD = 180^\circ$</p> <p><mdo:image src="ws3.png"></mdo:image></p> <p>A, B and C are points on the circle. O is the centre of the circle.</p> <p>Prove that $\angle AOB$ is twice $\angle ACB$</p> <p><mdo:image src="ws4.png"></mdo:image></p> <p>A, B and C are points on the circle. O is the centre of the circle.</p> <p>Prove that $\angle AOB$ is twice $\angle ACB$</p> <p><mdo:image src="ws5.png"></mdo:image></p> <p>A, B, C and D are points on the circle.</p> <p>Prove that $\angle ACB = \angle ADB$.</p> <p><mdo:image src="ws6.png"></mdo:image></p> <p>A, B, and C are points on the circle. The line AD is tangent to the circle.</p> <p>Prove that $\angle DAC = \angle ABC$</p> <p> </p> <p><mdo:image src="ws7.png"></mdo:image></p> <p>AB is a chord. D lies outside the circle on AB. C is a point on the circle. O is the centre of the circle.</p> <p>Prove that $\angle AOC$ is twice $\angle CBD$</p> <p><mdo:image src="ws8.png"></mdo:image></p> <p>A and B are points on the circle. The tangents to the circle at the points A and B meet at C.</p> <p>Prove that the length AC is equal to the length BC</p> <p><mdo:image src="ws9.png"></mdo:image></p> </mdoxml> 2 3 0 0 0 1 0