# NCERT Mathematics Class 9 Exemplar Ch 10 Circles Part 7

Get top class preparation for CBSE/Class-9 Science right from your home: fully solved questions with step-by-step explanation- practice your way to success.

Exercise 10.4

Q.1. If two equal chords of a circle intersect; prove that the parts of one chord are separately equal to the parts of the other chord.

Q.2. If non-parallel sides of a trapezium are equal, prove that it is cyclic.

Q.3. If P, Q and R are the mid-points of the sides BC, CA and AB of a triangle and AD is the perpendicular from A on BC, prove that P, Q, R and D are concyclic.

Q.4. ABCD is a parallelogram. A circle through A, B is so drawn that it intersects AD at P and BC at Q. Prove that P, Q, C and D are concyclic.

Q.5. Prove that angle bisector of any angle of a triangle and perpendicular bisector of the opposite side if intersect, they will intersect on the circumcircle of the triangle.

Q.6. If two chords AB and CD of a circle AYDZBWCX intersect at right angles (see Fig.10.18), prove that semicircle.

Q.7. If ABC is an equilateral triangle inscribed in a circle and P is any point on the minor arc BC which does not coincide with B or C, prove that PA is angle bisector of ∠ BPC.

Q.8. In Fig. 10.19, AB and CD are two chords of a circle intersecting each other at point E. Prove that

(Angle subtended by arc CXA at centre + angle subtended by arc DYB at the centre).