Mathematics 2000 JAMB Past Questions - Question 30: In the diagram above ,EFGH is a circle center of O.FH is a diameter and GE is a chord which meets FH at right angle at the piont N. if NH=8cm and EG=24cm ,calculate FH.

Correct Answer

C

Explanation

check solution in the diagram aboveTo find the length of FH, we can use the Pythagorean theorem.In the given diagram, FH is the diameter of the circle, and GE is a chord that meets FH at a right angle at the point N. Since FH is the diameter, it passes through the center of the circle O.We can consider the right triangle FHN, where NH is the height and FH is the hypotenuse. We are given that NH = 8 cm.Using the Pythagorean theorem, we have:FH² = NH² + FN²Since FH is the diameter, FN is equal to the radius of the circle, which is half the length of FH. Let's denote the radius as r.FN = rSubstituting the given values, we have:FH² = (8 cm)² + (r)²Now, let's consider the chord GE. We are given that EG = 24 cm. Since GE is a chord that meets FH at a right angle, we can use the property that the product of the segments of intersecting chords is equal:FN * NH = EN * GNr * 8 cm = (12 cm) * (12 cm - r)8r = 144 - 12r20r = 144r = 144 / 20r = 7.2 cmNow, we can substitute the value of r into the equation for FH²:FH² = (8 cm)² + (7.2 cm)²FH² = 64 cm² + 51.84 cm²FH² = 115.84 cm²Taking the square root of both sides, we get:FH = √(115.84 cm²)FH ≈ 10.77 cmTherefore, the length of FH is approximately 10.77 cm.