AB is a diameter of a circle of radius 5 cm. Let P and Q be two points on the circle so that the length of PB

Question

AB is a diameter of a circle of radius 5 cm. Let P and Q be two points on the circle so that the length of PB is 6 cm, and the length of AP is twice that of AQ. Then the length, in cm, of QB is nearest to

Select an option to reveal the answer and explanation

Accepted Answer

9.1. Since AB is a diameter, AQB and APB will right angles. In right triangle APB, AP = 10 2 − 6 2 = 8 \sqrt{10^2-6^2}=8 1 0 2 − 6 2 ​ = 8 Now, 2AQ=AP => AQ= 8/2=4 In right triangle AQB, AP = 10 2 − 4 2 = 9.165 \sqrt{10^2-4^2}=9.165 1 0 2 − 4 2 ​ = 9.165 =9.1 (Approx)