Chapter 10 : Tangents to a circle

Exercise - 21

Q. 1. Two circles intersect at A and B. From a point P on one of these circles, two lines segments PAC and PBD are drawn intersecting the other circles at C and D respectively. Prove that CD is parallel to the tangent at P.

Q. 2. Two circles intersect in points P and Q. A secant passing through P intersects the circles at A an B respectively. Tangents to the circles at A and B intersects at T. Prove that A, Q, T and B are concyclic.

Q. 3. In the given figure. PT is a tangent and PAB is a secant to a circle. If the bisector of intersect AB in M, Prove that: (i) (ii) PT = PM

Q. 4. In the adjoining figure, ABCD is a cyclic quadrilateral. AC is a diameter of the circle. MN is tangent to the circle at D, Determine

Q. 5. If is isosceles with AB = AC, Prove that the tangent at A to the circumcircle of is parallel to BC.

Q. 6. The diagonals of a parallelo gram ABCD intersect at E. Show that the circumcircles of touch each other at E.

Q. 7. A circle is drawn with diameter AB interacting the hypotenuse AC of right triangle ABC at the point P. Show that the tangent to the circle at P bisects the side BC.

Answers