AB is a diameter and AC is a chord of the circle with centre at Q. the radius parallel to AC intersect the circle at D. Prove that D is the mid-point of the are BC.

AB is a diameter and AC is a chord of a circle with centre O such that angleBAC=30^@ . The tangent at C intersects AB at a point D. Prove that BC=BD.

AB is a diameter of a circle with centre O and AC is a chord . The straight line through O parallel to AC meets the arc BC at D. Prove that, BD= CD.

AB is the diameter and AC is a chord of a circle with centre O such that angle BAC=30^(@) . The tangent to the circle at C intersects AB produced in D. Show that BC=BD.

ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that D is the mid-point of AC

ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that D is the mid-point of AC.

Seg AB is a diameter of a circle with centre P. Seg AC is a chord. A secant through P and parallel to seg AC intersects the tangent drawn at C in D. Prove that line DB is a tangent to the circle.

In Delta ABC, AB = AC. A circle is drawn with diameter AB and it intersects BC at D. Prove that D is the midpoint of BC.

AB is a diameter of a circle with centre O. Chord CD is equal to radius OC. AC and BD produced intersect at P. Prove that : angleAPB= 60^(@)

ABC is a triangle right angled at C and M is mid-point of hypotenuse AB. Line drawn through M and parallel to BC intersects AC at D. Show that: MD is mid-point of AC.