Mathematics
In the given figure, AB is a diameter of the circle. Chords AC and AD produced meet the tangent to the circle at point B in points P and Q respectively. Prove that :
AB2 = AC × AP
Related Questions
In triangle ABC, ∠BAC = 90°, AB = 6 cm and BC = 10 cm. A circle is drawn inside the triangle which touches all the sides of the triangle (i.e. an incircle of △ABC is drawn). Find the area of the triangle excluding the circle.
Use ruler and compasses for this question.
(i) Construct an isosceles triangle ABC in which AB = AC = 7.5 cm and BC = 6 cm.
(ii) Draw AD, the perpendicular from vertex A to side BC.
(iii) Draw a circle with center A and radius 2.8 cm, cutting AD at E.
(iv) Construct another circle to circumscribe the triangle BCE.
In a triangle PQR, L and M are two points on the base QR, such that ∠LPQ = ∠QRP and ∠RPM = ∠RQP. Prove that :
(i) △PQL ~ △RPM
(ii) QL × RM = PL × PM
(iii) PQ2 = QR × QL