Question

P is a point on a circle whose longest chord is AB. If P doesn't coincide with A or B, then $\angle APB=$ .

• A. 80${}^{\circ }$
• B. 75${}^{\circ }$
• C. 90${}^{\circ }$
• D. 100${}^{\circ }$

Answer 1

The correct option is C 90${}^{\circ }$


Consider the circle as shown, with centre O and AB as the longest chord. Since diameter is the longest chord, AB is the diameter.
Hence $\angle APB={90}^{\circ }$
[$\because$ angle in a semicircle is 90${}^{\circ }$]