NCERT Class 9 Solutions: Circles (Chapter 10) Exercise 10.6 – Part 5
Q-9 Two congruent circles intersect each other at point P and Q. Through P any line segment APB is drawn so that A, B lie on the two circles. Prove that QA=QB.
Since PQ is common chord
Angle subtended by arcs of equal lengths on congruence circles must be equal, therefore,
Therefore in isosceles triangle AQB,
Q-10 In any triangle PQR, if the angle bisector of and perpendicular bisector of QR intersect, prove that they intersect on the circumcircle of the circumcircle of triangle PQR.
PQR is a triangle inscribed in a circle with centre at O, A is a point on the circle
PA is the internal bisector of and B is the mid-point of QR
BA is the right bisector of QR
In , since both the arcs QA and AR subtend equal angle at the circumference ( .
Therefore in triangle QAR,
Therefore, by SSS criterion of congruence,
Hence, (corresponding parts of congruent triangles)
Therefore, BA is the right bisector of QR.