Question

Q1.Two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that angleAPB = 2 angleOAB.
Q2. In a circle of radius 17 cm , two parallel chords are drawn on opposide sides of diameter.The distance between two chords is 23 cm and length of one chord is 16 cm , then the lenth of the other chord is.....

Q3.Prove that in two concentric circles the chord of the larger circle which touches the smaller circle is bisected at the point of contact.

Answer 1

first join A and B and u will get two different triangles , both of these would b isosceles triangles , the first one would b triangle AOB where OA and OB r equal in length ( they r the radii of the circle) ; the second triangle is APB where PA and PB r equal ( properties of tangents )

the property to b used is the tangent makes an angle 90 with the radius ie. angle OAP = angle OBP = 90 degree

and with this u can prove the statement